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.