Pretty much every train I’ve ever boarded at Penn station was empty when it pulled in. Trains that come in with passengers discharge them then leave for service.
In the Long Island direction, trains are most often coming from the West Side Yard, which is what Hudson Yards was built on top of.
In the New Jersey direction you have a higher chance of encountering a train with passengers on it, because they use Sunnyside Yard in Queens for this purpose, but the yard is often at capacity or the tunnels leading to them are, so those trains may need to turn around in Penn instead.
