So, you're bidding for the equity, as other bidders will be also, not the full property value.In the second scenario, you're simply a junior lien holder, and if you foreclose, you're only entitled to what you're owed, of a third party buys it.  

This means:Even though the tax card states that Bank of America is the lien holder, there's a possibility they've disposed of it (selling their non-performing note) prior to initiating or during the foreclosure process. 

The borrower is the "title" holder.

A sub2, then negotiate a short pay off as the title holder....maybe, but not common.

An escrow account is an account where funds are held by a third party, for distribution (ie. funds from a buyer are escrowed at the title co. for delivery to the seller a and lien holders, or monthly payments go into an escrow account for taxes and insurance, etc).  

There are advances that are typically made to preserve the property and its title and keep other potential lien holders from gaining superior status to the security instrument like property taxes.  

@Mark Ainley  much of the financial crisis was caused by exactly your thought process,, IE when many 5 year commercial loans came due the lenders either were not in a position to re write ( they went under and the new  bank that acquired the failed bank  or note holder would not re write the loan.. its was a major cluster for many companies that would in the day had no issue with a rewrite of their paper..

You may be able to negotiate a modification with the fist lien holder after foreclosure, but its a risky gambit at best.  

The toilet paper holder spindle sprung out of her hand and went into the toilet just as the water was going down.

The new note holder plans to foreclose/auction the property soon and wants to know if I am interested to buy.