Any lien which grants an interest with an enforcement remedy of foreclosure can foreclose if the conditions to do so are met. Payment default, is one of those standard conditions although there are others.
The establishment of seniority, usually through time (date of recording) has priority over interests that are granted or taken, later in time. Seniority in most cases, is first in time, first in right. What is essentially happening when a borrower (mortgagor) gives a lender (mortgagee) a security interest, is a granting of superior (to the mortgagor) interest in the equity of the property. To that extent, the mortgagor essentially subordinates their right to defend title to the property. By law however, the mortgagor retains a right of redemption. Since property equity is not infinite, each interest granted results in equity being reduced. Usually, we see the first interest granted being the most equity reduced. Continue in succession and reduction. When equity is present, the interests are secured, when equity is not present, there is no security.
Right of repayment from the real property sale by foreclosure (distribution) is defined by seniority and is in succession of time as a chronological order which creates level of seniority. (Some interests, like those of the Federal Government, have a legal superiority by law regardless of order in time of lien) A first mortgage, is only first because there is no interest granted before them. The second mortgage, is second because before it is a first mortgage, etc.
Imagine if you will, title to the property is simply a line from left to right. At the very left or starting point of the line is where the property owner takes ownership. Let's define that as B(0). Any event prior to (left of) B(0) is essentially why you get title insurance. It is assumed at B(0) all equitable and legal rights are bundled up in 100% and sold to the new owner. Anything prior to B(0) would mean, that 100% bundle is fragmented or less than 100%. The next event, let's say it is a mortgage, then becomes M(1). The next event, assume another mortgage is then M(2). And for example sake, let's throw one more on there, a third mortgage in M(3).
So, here is my little text timeline:
|-----------|-------------|---------------|---------->
B(0) M(1) M(2) M(3)
The M(2) is superior to M(3) but inferior to M(1). If conditions are met for P(2) to initiate a foreclosure, such as payment default, they can then do so which is granted by the mortgage and note. The action of including all parties (B and all M's) is called "joining". Foreclosure is the act of extinguishing rights of redemption on the joined parties. If a party is not joined, those rights can not be foreclosed (extinguished). (an important idea to understand as a junior lien holder) If a foreclosure only joins the mortgagor, then the rights of the junior liens were not extinguished, however in most cases, their junior lien holder does not 'improve' their rights. Further, the legal right to extinguish redemption (foreclose) is only for subsequent interests granted. That is, M(2) can only extinguish rights of redemption for M(3) and the mortgagor B(0) but can not extinguish the right of redemption for M(1). Since M(1) is the most senior, there is nobody to redeem from. This is where "Subject To" sort of comes from. The junior mortgagee M(2) has an interest in the property Subject To (inferior to) M(1).
Each time the mortgagor grants a new interest, they in essence move to the right (inferior) of the mortgagee. To that extent, the mortgagor is Subject To the Mortgagee. So when M(1) is granted:
|---------|------------->
M(1) B(0)
Then when M(2) is granted, in essence the following occurs:
|------------|---------|------------->
M(1) M(2) B(0)
*Remember, these lines are first in line, first in right which is usually defined by time.
However, each time and in most cases, each subordinate interest granted retains a right to redeem. So B(0) retains a right to return to its original amount of right to the equity in the first line but only if the granted interest (M1-3) is extinguished.
These concepts are also why any deed from mortgagor to a new owner would also be inferior to all things prior in time. The equity remaining has diminished, thus the new party can only get what is left. So if the mortgagor deeds to a new party without satisfying or extinguishing the interests of the prior parties, the new owner is still an owner, they just do not have equitable and legal rights greater than those before it.
A junior lien can not force a senior lien to foreclose. So M(2) can not cause M(1) to extinguish (or attempt to) extinguish the right of redemption of M(2). Now, M(1) may do so at their will, provided breach has occurred. However, M(1) has no fear of loosing its superior interest in the property in the event of M(2) foreclosing since M(2) can only extinguish rights inferior to theirs along with the mortgagor.
In the event M(1) forecloses and M(1) joins M(2-3), then any surplus from sale automatically accelerates and M(2-3) rights to the property are discharged. There is a caveat where if the mortgagor redeems, where they would only be redeeming M(1) then M(2-3) would be revived to their equity in the property, to that extent, equity is re-established. A redemption is a redemption only if the party had a prior interest (say through a mortgage) in the property.
If M(2) chooses to foreclose, it can not foreclose M(1) but it can foreclose M(3). When M(2) has its foreclosure sale, it is the lien that is the subject of the sale. As such, it has priority of distribution. Priority of distribution is the seniority established by title to the real property. So M(2) gets distributed first and M(3) gets what's left over and then the borrower, if any. Notice, M(1) actually get's nothing. This tends to be the confusing idea for some. Since M(1) doesn't stand to loose it's equity by way of M(2) foreclosure, it is not joined in the equity from M(2) forward (M(3) and B(0)). So, M(1) stays in place and any ownership of the property is then "Subject To" (inferior to) the interests and rights of M(1). So a bidder at auction who exceeds the minimal bid given by M(2) 'wins' title to the property subject to M(1). If nobody bids, then M(2) takes back title in exchange for the satisfaction of it's debt. As such, M(3) and B(0) are wiped out and get nothing since nothing was paid. M(3) is still a debt owed but is not secured by the property any longer. Both M(3) and B(0) still have a right of redemption subject to the time defined by law they can exercise said right.
Sometimes, M(2) can call for M(1) to be a necessary joined party so the balance due is officially calculated by court or trustee. This gives bidders at auction formal insight into the total amount due to gain clear title. Under the guise of those same definitions, M(3) is a proper party joined. So, M(1) is necessary to illustrate the path to clear title and M(3) is proper as they have to extinguished to grant title from M(2) forward. In that case, title may not be clear since M(1) is still in place.
Because M(2) act of foreclosure may result in Subject To title. They may choose to not to finish foreclosure and wait for M(1) to foreclose and exerciser their right of redemption.
When M(2) chooses to redeem, one of three things happen:
(1) M(2) gains the rights equal to that of a third party buyer at auction, if no further redemption occur through expiration, then those rights turn into title.
(2) M(2) simply causes the foreclosure judgement to be avoided. M(2) can then add the proceeds used to redeem to the balance owed and seek foreclosure with the new sum.
(3) M(2) becomes subrogated to the rights of M(1)
The term subrogation is the substitution of one person to the position of an obligee whose claim he has satisfied. The result of subrogation is that the person subrogated stands in the shoes of the one whose claim has been discharged by his performance. He succeeds to all of the rights, priorities, liens and securities of the former obligee.
Great, now it is important to note, each state uses some form of the above but not all. So redemption rights are not the same in every state, you need to understand what those are for the state the mortgage is in. As such, redemption periods are not the same in all states. They may expire before or after sale by varying times. Also, state specific.
So to the OP Questions:
1. The idea of no equity, would likely mean no bidder at auction. So then, the mortgage you hold would be extinguished and those rights would convert into title. The new rights in title are Subject To, the rights held by the first mortgagee. The first mortgagee is still entitle to it's payments and the lack thereof does mean default and possible foreclosure. There is contest in some states whether a first lien must recognize a junior lien holder as a successor in interest and thereby not be able to trigger Due on Sale. This same idea also applies to whether the first mortgagee has a duty to accept payments on the obligation since the paying party (you) is not a party to the mortgage contract they hold. So you could find the first demanding full payment or they foreclose or you could find the first willing to accept payments. Mind you, if you are not considered a successor in interest, then technically you would have to formally assume the mortgage which can only be granted by the Mortgagee.
2. As explained above, (towards the bottom, I know it's long), if the second forecloses it should properly join all junior lien holders, those parties will be the parties who are distributed funds from sale. The first mortgagee is not joined in equity in the foreclosure of a junior mortgagee thus they do not get distributions. This is because they retain their superiority in title and equity.
3. As a new junior mortgagee, you have no obligation to any superior interest. That is, no obligation is created under the law through the process. Unless, you actually assume the mortgage in superior position, you are not obligated or liable under the debt. However, if you do not take steps to protect your interests, the senior mortgagee can foreclose and you loose your investment.
I know, it's a long post. But it is beneficial to the populous to have a fairly thorough explanation. Welcome to the world of mortgages.