Most rescues will require that you sign a contract. Numerous points are often outlined in the document, and they vary per rescue group, but one thing that is often included in the agreement is if you need to give the dog up for any reason the dog must be relinquished back to the rescue. This helps them ensure that the dogs they’ve helped rescue, rehabilitate and adopt out do not end up back in a shelter for any reason.
The rescue will also have the microchip permanently identified with that dog. Some will require that the microchip always be linked to the rescue, and others will allow you to change it to your personal information after a certain amount of time.