"Subject to" problems down the road

[Amy A.]

I have been searching BP for over an hour, and I apologize if this topic has been covered, but I can't find an answer anywhere. 

When you sell a home that has a mortgage, you often have to sign documents to get your mortgage paid off, such as a payoff demand letter sent by the title company to the lender.  How does this work if you have a "subject to" deal and the previous sellers, who have the mortgage in their names, are long gone?  

I have a possible deal where I want to hold the property for a year, rent it, paying the "subject to" loan (yes, I know the lender could give me a 30 day notice to pay off), and then fix and sell it.  I don't want to have problems selling the property and am not willing to seller finance it.

Are there other title issues with "subject to" deals that aren't often discussed in the forums or podcasts?

I see that insurance issues are often glossed over, but they have been discussed somewhat in the forums.

Thank you.