Here's what I see.
You sign over the deed, they rent out the house on a lease to own where the renter pays a higher rent and deposit the difference of the higher rent also goes towards down payment. You are still on the mortgage/note so ultimately you are responsible for the mortgage so if stuff stops happening the foreclosure and bad credit falls on you. If the lease to own folks do not live up to the terms of the Relief Co. they are evicted and lose what ever they put into the home and the cycle continues again. Sure they say they will make the mortgage payment and they might, but for how long, as long as their rent/lease to own checks come in. What happens when they are not receiving these? Call me cynical on these deals but there always has to be a catch.
Unless the lender releases you from mortgage/note or the home is sold in the end you will be on the hook no matter what happens on this. Remember you will be signing over the deed so you will not have any rights or say on the property once you do this but you will still be responsible for the mortgage note. HTH
I don't see how the math works in the first place. In most areas, an underwater mortgage payment and cost to maintain are going to be more than what they could collect in rent.
I'll bet they are making money with lowball settlement offers to the mortgage company (Look! Your borrower doesn't even own this property anymore!) and then trying to flip it the rent-to-owners types that they apparently get. The problem with that is banks are reluctant to agree to short sales (or settlements) on performing loans. That makes me wonder about their promise to keep up with the mortgage payments.