Without a paper trail, whose to know if she is purebred or not?
It takes one less generation for Genetic Recovery than Jersey Expansion. By the 4th generation the calf is in the herdbook. 5 generations with Expansion as the first step.
It isn't as big a deal in the Jersey world as it is in the Nubian world. Jersey breeders don't tend to be as sticky about papers. Heck, they are using and selling
PR bulls. Admittedly that is because it was found there was Holstein in a dam that sired a number of bulls in the lineups. They are still being used even though those offspring will not be in the Herd Registry but rather in the Genetic Recovery.
If Jerseys are that rare, then even an unregistered Jersey should do just fine. When buyers are looking for family cows, registration papers are usually last on their list. Health and handleability are by far more important.
If you are willing to work with issues, you can usually get ahold of older registered cull cows if you want the papers. You need to know what you are doing though.
Farmers may retain all the heifers, but at some point, they have to sell animals. At least at that point, it is better known how she is and what her udder is like.
We have rarely sold heifer calves and bred heifers. We sell first calf heifers though because we know how her udder is and her demeanor at that stage.