Being “close to the money” is irrelevant. After all, how would you decide how close is close enough? Similarly, stack size is irrelevant.
There’s no rule stating that an absent player could be penalized merely because of their absence. Therefore, once a player has bought in, they are entitled to be absent as long as they want.
Bottom line, the stack remains in until blinded off. If the stack manages to make it into the money while being blinded off, so be it. The prize money will be set aside until it can be given to the player.