Emily mentioned: "In my experience, what raises the red flag to the lender is if you set up a 3rd party co. & now that's where the payments are coming from & suddenly Not from Mr. & Mrs. Smith. It appears to the bank that the property has sold when they know it hasn't."
Actually, most such transactions are put through a "holding company" ( Similar to an escrow.) where the buyer makes them the monthly payment, and the holding company disburses payments to the lender(s), taxes, and to the seller.
If the lender questions the holding company, they would usually say that the owner/seller has made the property into a rental, and that they are the owner's "property management company".
So, it CAN be a reasonably safe and viable transaction - it just needs to have an attorney give his or her blessing on it. We did such transactions a lot in the 70's, and they seem to be coming back, again.
Nothing to be afraid of - just careful.