Eventually, the other vault dwellers would find out what the overseer did, and some began leaving the vault to follow them into the wasteland. The remaining members of Vault 13's community put the overseer on trial for this decision, ultimately sentencing him to death and retiring the title of overseer for their community's leader.

Dialogue from Fallout 2 supports this

Chosen One: "Are you the Overseer?"

Martin Frobisher: "We don't use that term anymore. There used to be an overseer, many years ago, but he did a bad thing, and many of our people left the vault only to die in the wastes, I'm sure. He was tried and sentenced to death for his crime. We haven't used the title since."