I can't remember whether Jorah was exiled before or after Jeor abdicated. But whether or not he did, Jeor himself says that it's not good for men of the Night's Watch to return home. If he knew he would not be going back to Bear Island, would it not make more sense for him to leave Longclaw with Jorah or Maege, thus ensuring its continued place as an ancestral sword?
I believe he had already taken the black and given Jorah Longclaw. But when Jorah was exiled he left the sword behind with his family. In the TV show, Jeor explicitly mentions that "At least Jorah had the decency to leave it behind."
Jeor's sister and nieces sent it to him at the Night's Watch. I assume he would have held onto it until one of his daughters had a son, but since he was quite old and they did not seem to be having children he gave it to Jon Snow instead as a gift for saving his life.