This is addressed in the Transfer of Ownership Agreement both you (the private owner) and the adopter will be signing prior to the adoption being finalized. In this agreement, it states the following under the Adopter Signature portion:
If at a later date I am unable or unwilling to keep this Pet, I agree to first immediately contact Owner and give them the option to reclaim the Pet at no charge. If I ever need to rehome this Pet. and Owner cannot reclaim this Pet, I agree to try in good faith and using my best efforts to find a new home for this Pet while keeping him/her in my home, and to always act in the best interests of the animal.
If you have any other questions regarding this, please email rehome@adoptapet.com!