It is possible to register a dog without any registration papers from the seller. An owner must provide proof that the dog in question has a lineage that goes back to registrable stock, with no breaks in the line.
The American Kennel Club allows owners to apply for registration for a dog without papers, and as long as they can determine the dog is a purebred, the dog can be registered. Owners must provide proof of pedigree, such as the parents' information. If the owner has proof of registration from another company, that can be sent in lieu of the registration application from the AKC.