During play, they return to the supply unless the effect explicitly says otherwise. (The exact formatting of "Call Forth Predators" in earlier printings of Branch and Claw implies otherwise, but the Jagged Earth rulebook explicitly states on page 28 that this is the general rule going forward.)
Most pieces aren't component-limited, so this doesn't usually matter one way or the other. Nevertheless, it's occasionally relevant for a few cases with piece limits: