Made me start wondering if supplies could be picked up in route. The oort cloud (https://en.wikipedia.org/wiki/Oort_cloud) extends most of the way to the next star and presumably extends a similar distance away from the next star. Missions would need to be sent out in advance of the ship to start collecting and making fuel. It could then be accelerated up to catch the generation ship. It seams easily plausible in a science fiction sort of way.
Generation ships can't slow down. They don't have the fuel to slow down and start back up, only to stop at the end.
Also, the supplies should be available in the home system. It costs just as much to send out probes and accelerate the supplies as it does to send the supplies with the ship.
The only exception is that don't have water as fuel, and could travel slowly to the closest icy object, and then do the full burn to speed. It would add years though.
