The new purchaser makes monthly payments to the seller, who is then responsible for making the payments to the underlying mortgagee. Should the new purchaser default on those payments, the seller then has the right of foreclosure to recapture the subject property.
Because wraps are a form of seller-financing, they have the effect of lowering the barriers to ownership of real property; they also can expedite the process of purchasing a home. An example:
Typically, the seller also charges a "middle" on the first mortgage. For example, one has a first mortgage at 6% and sell the whole property with a rate of 8% on a wraparound mortgage. He/she make a 2% middle on the first mortgage amount, using other people's money to make money. So, it is in the best interests of a seller to keep the wrap, rather than allow the buyer to assume the first mortgage.
As title is actually transferred from seller to buyer, most wraparound mortgage transactions will violate the due-on-sale clause of the underlying mortgage, if such a clause is present.