Paranoid, nervous, and usually careful, Prosper was a smuggler, ferrying several large cargos of ingots from the steelyard of The Pitt to outlying areas. His operation was soon compromised and his crew mostly butchered. The survivors were sold to slavers heading toward Paradise Falls.
Into The Pitt: The Lone Wanderer can buy him and the other slaves in the slave pen from Ramsey or all the slavers can be killed to get the key to open the pen. After either option Prosper can be talked to and his clothes taken from him or the clothes from the dead slave in the corner.
If he is followed, he and the two other slaves will try to head to the entrance of Vault 101. They will likely be killed if not escorted, although they can survive the journey at which point they will "live" at the entrance of Vault 101. After some time though, he will disappear from the game.
He will not equip any weapons or clothes given to him via reverse-pickpocketing, meaning his chances of survival cannot be improved whatsoever.
If the Lone Wanderer asks Prosper for the clothes off his own back the dialogue option reads, "Your clothes. Give them to me. Now." This is a reference to a recurring line in The Terminator movie series.
His name is fairly ironic, as Prosper vaguely means to have good fortune and a happy life, which is obviously not the case when he is encountered.