Are animal shelters allowed to adopt your dog out before the grace period is up?

No they are not and for good reason, this grace period provides the owners with the opportunity to come and reclaim their dog. After all not every dog at the shelter has been abandoned by their owners, some are beloved family pets, who ran away or got lost and is sorely missed. The best thing you can do if the dog you are interested in isn't up for adoption quite yet is to let the shelter know that you are interested and ask them to contact you if the dog hasn't been claimed at the end of the grace period.