It's not necessarily a scam, but be careful.
When legitimate, it's called a "Subject To" (or "Sub 2") transaction. Here's how it works:
First, keep in mind that a mortgage and a deed are two separate items. A mortgage is the IOU that you signed promising to pay the lender for the property. The deed is the document saying you own the house. Normally, they "travel" together. You buy a house: You receive the deed and you're responsible for the mortgage. A "Subject To" separates them.
In a "Subject To," you deed your property to someone else, but remain responsible for the mortgage. That is, the investor acquires your house "subject to" the existing financing. The investor promises to take over payments, cover any back payments owed, and ultimate sell or refinance the property, eliminating the current mortgage.
It can be totally legitimate. I know investors who do this. The benefit to you is that the investor makes up your back payments, takes over payments, and ultimately sells/refinances, removing you from the mortgage. The benefit to the investor--when there's equity in the property--is that the investor acquires the property for only the amount he/she has to pay in back payments and arrearages. The investor hopes to rent your house out to someone who will pay more than the current mortgage payments, thereby picking up some cash flow. And, when the investor sells the property, he/she receives the equity in the property.
It's risky for you because you're giving up ownership of the property but remaining responsible for making payments on it. You've got to trust that the investor will live up to his/her end of the deal.
Regarding the due on sale clause: Subject Tos violate the due on sale clause. If your mortgage contains a due on sale clause (and most due), and if the lender finds out that equitable interest in the property has been transferred without its approval, then the lender has the right to call the mortgage due and payable. No doubt about it.
Will the lender find out? Probably not, if the investor knows what he/she is doing. If the lender does find out, will it call the mortgage immediately due and payable? During the recent hot market, a few would. Many wouldn't. Today, very few will. After all, from the lender's perspective, which is better: An investor who made up the arrearages and is paying the mortgage on time, or calling the loan, possibly leading to a foreclosure and a bank-owned property. Many will "look the other way" and let someone, anyone, keep making the payments.
If you consider going that route, ask the investor for references. That means several people/owners who've participated in similar transactions with the investor. Also, as far as references, ask the investor for the names of his lawyer and accountant. And check with the investor community in your area. In most areas, many investors know each other. Reputations--good and bad--spread fast. Other investors will know who the scammers are, and who the legitimate ones are.
Hope that helps.