When the Vault's only functioning water chip was damaged and shut down, he sent one of the vault dwellers, who later became known as theVault Dweller, into the wasteland to find a replacement chip. In the course of his adventure, the Vault Dweller ended up defeating the mutant threat, and was subsequently expelled from Vault 13, as Jacoren thought that he would ruin the Vault Experiment by convincing people to leave the Vault.
Despite the Dweller's exile, many people chose to follow him into the Wasteland. Jacoren's fate after said event is not made clear. He can try to stop those who want to leave and eventually be tried and sentenced to death for his crime, probably after the dwellers learned about his involvement in the Experiment, or he can be killed at the hand of the Vault Dweller after the goodbye speech.
He was fully aware of the Vault Experiment program conducted by the Enclave, and therefore tried to do everything to keep Vault 13 closed for 200 years, just as the program dictated. As it is quite unlikely that he could have been more than 100 years old, the knowledge about the experiment was probably passed to him from the previous Overseer, most likely one of his parents.
With the Bloody Mess trait, the Berserker or Childkiller titles, or a low reputation, right after the Overseer's goodbye speech at the end of the game, the Vault Dweller will automatically put away any held weapon, draw a pistol and shoot the Overseer in the back. It is also possible to kill Jacoren by initiating combat just after his speech, and putting him down with one or more shots. If Jacoren is killed, he falls to the ground with his internal organs hanging from his body, with both his left arm and left leg severed and his ribcage exposed, whereupon he uses his remaining arm & leg and crawls in an attempt to move to the Vault door, which he does reach but is unable to open before ultimately succumbing to his injury.
I always thought of Fallout's story of drawing straws was something the Overseer thought of. "Look, someone has to go outside, and they may die out there, so let's draw straws". Someone, probably not the Overseer since he wouldn't have gone outside no matter what, demanded that EVERYONE draw a straw in order to be truly fair. But to be honest, the vault dwellers were simply terrified of going outside, and terrified people do not always make the wisest decisions. Anyway, when big dumb Larry drew the straw, maybe the Overseer saw a way to rid their limited gene pool of some really bad alleles. - Tim Cain at DAC forum
At the end of the quest Trouble on the Homefront in Fallout 3, Amata has the same quote as Jacoren saying, "I'm sorry. You're a hero... and you have to leave", right after she exiles the Lone Wanderer from Vault 101. However this is only if the Lone Wanderer kills the Overseer, if they convince the Overseer to allow the vault to open, she will be thankful for their help but will reluctantly exile them due to the other vault residents blaming them for the problems in the vault.