WW, here's a common misconception people have about deeds. A deed is an instrument that conveys title. In the same way that you can't have your empty car come and pick you up, you can't convey somebody else's title to yourself - the person that the property was deeded to has to do the conveying.
Similarly, you don't "get people off" the deed. The new deed takes precedence over the old one. The old one is still in the records, this way we form a "chain of title," that we can search to ensure that there aren't any former owners out their with claims to the property.
But to answer your question - you heard wrong. And the scheme that David & Ken correctly identify really requires that the value of the home warrants taking over the mortgage - you don't want to take over a home that's underwater, and if it's not underwater, the owner will likely be better off selling it and pocketing a few dollars.
All the best,
When banks give you a mortgage loan these days, they almost always leave out the 'Assumption Clause' which would allow the original borrower to transfer the mortgage to another person. But there's almost always a paragraph of fine print somewhere in the mortgage documents that's called an 'Alienation Clause'. What this means is that if the bank catches the original borrower trying to do this, the bank has the legal right to demand PAYMENT IN FULL of the entire mortgage. Since the original borrower obviously doesn't have the full amount (cause if he did he would have paid off the mortgage), the bank can claim the original borrower is now in default, and start foreclosure proceedings.
Your best bet is to show all your paperword to a real estate attorney and let them decide.