The Vault 13 rebels are a small, vocal minority of the Vault population that is considering life on the outside world as of 2162.
Before the adventures of the Vault Dweller, charismatic vault local Albert Cole led the rebel faction. Seeing as he is one of two possible identities of the Vault Dweller, it is possible that Theresa took his place as leader upon his departure for the outside world in search of a new water chip.
As time went by and the Vault Dweller hadn't returned, the movement to leave the vault grew stronger. Water supplies were running low. Although the Vault Dweller had returned from the wasteland with a replacement chip, the rebels continued to argue that an exodus would be in everyone's best interest.
Upon the Vault Dweller's exile, many vault dwellers belonging to the rebels followed him to the outside. The former rebels played a crucial part in building the village of Arroyo.