A Subject-To deal involves transferring title without the seller paying off their mortgage. The deed should be a Special Warranty Deed, (or an All Inclusive Deed in some states) that warrants title except for the encumbrance created by the mortgage. Title is transferred subject to the underlying mortgage being paid as agreed.
This is very risky for the seller as the mortgage is still in their name, late payment of failure to pay becomes a credit issue fr that seller. To do these properly the seller must sell taking a security interest as if the were a lender, this gives the the right to foreclose. Since the agreement to pay the mortgage isn't an assumption of the loan with consent of the lender, the obligation to pay become a civil matter, the seller can sue for damages if a buyer dings their credit and that can be a significant claim to pay for the bad buyer.
The buyer also has risks that the lender will find out and call the note due under the due on sale clause. Little known fact is that many lenders, banks and loan servicing companies must call the note upon discovery. The reasons have little to do with payments being made or interest rates, especially with secondary market loans. There are title, foreclosure and credit issues for the lender.
For this reason, Sub-To deals should be short and sweet, the longer these arrangements continue the higher the risk that a lender will discover what was done. 12 to 18 months is long enough to play with, IMO, as upon discover the foreclosure clock can be started and this time frame usually allows enough time to sell or refinance to payoff that demand.
A buyer should always be prepared to payoff the mortgage taken, by sale or refinancing or just pay it off!
Renting the property is usually fine, giving an option to a tenant buyer gets tricker, That is another subject. What you do can effect your ability to sell or refinance out of your Sub-To, so the use and future agreements, encumbrances that you may create matters!
In the old days, making up payments and avoiding foreclosure was common, today pre-foreclosures and delinquent or slow paying borrowers are on a lender's radar screen. For them, there are red flags that point to a disguised sale, insurance, tax bill changes, new names paying the payments as well as increased loan audits internally. This is not a good method to go into a foreclosure deal with.
If a seller does have equity, that may be financed on top of the mortgage taken, a wrap of the underlying mortgage and equity.
Any financing agreement is a bilateral contract and that may not be assigned to another party without consent of the lender, this is basic contract law. That means you can't wrap a deal, bump the price and wrap it again to another buyer by assignment. Besides, that causes amortization and interest rate violations and doing weighted average financing is beyond the scope of mortgage originators or investors for loan/lending compliance. If you sell, just do a clean sale to a new buyer.
A Sub-TO can become an installment sale, there are tax ramifications for the seller to recognize the sale and taxable amounts being due, so a seller that just walks away can have problems (example where they obtained a second mortgage for cash).
This is probably more than you needed to know right now, these really aren't for a newbie investor to walk through alone. You really need to learn real estate and a bit of financing before this tactic is attempted. Good luck :)
