To expand on C_Watson's answer, most folks cut the throttle back on a dive, so the engine doesn't need all that much fuel. Most dives are only a few seconds, so the fuel in the fuel line is plenty to keep the engine running. But, in theory, you could starve the plane for fuel if you were diving long enough.

The problem with letting the clunk come forward is that on most tank designs, once it gets forward, it won't move back. I don't think there's any particular reason not to design a tank so the clunk can come forward, they just don't.