What is the advantage to a bank in selling a note vs. foreclosure?

Just to refine this a bit more, the short sale process is usually begun by the homeowner and he tries to get the bank to agree to the process.

So a note sale is done by the bank, and a short sale by the homeowner?

I wonder if there is a way for me to get my loan sold to someone as a note sale?
I am struggling to continue the payments, but would be fine if I could just get my payment lowered by $400.00 a month.

Fannie Mae won’t work with us because we haven’t missed a payment. They’re going to force us to quit making payments and we don’t want to do that. We have tenants, so that would hurt them and our credit.

Yes, but in the latter case the bank has to agree to it, whereas the homeowner doesn’t have to agree to sale of a note.