If your loan is an adjustable rate mortgage or an FHA loan, it is, most likely, an assumable loan.
The new buyer will have to qualify for that loan through that company. There is usually a processing fee charge of up to 2% on that. Your current mortgage servicer can answer as to whether or not the loan is assumable and will send you out a package to have the buyer complete.
You will then be removed from liablity on the loan and can move on with out any future headaches.
If your loan is not assumable, then, you will be going on pure trust!
If you deed the property to the buyer and allow them to make your mortgage payments you have no control over the property.
Make certain that you still are on the title ( maybe at 1/2% interest) and that you have the new owner send you the payment that you forward to the lender. Once the new owner establishes that they are trusted to make the payments, you can lighten up on that specific requirement.
Once the new owner is on the title of the property for 12 months and payments can be documented, they will be eligible to refinance the home.