Movement in z-axis

Really simple question. A screw fell our from somewhere inside our Carvery and we’re trying to work out where it came from.

Does the motor normally have play in the z-axis? Meaning with the machine turned of can you usually move the motor\spindle up by about 1/2", with no resistance. It’s just sitting down under it’s own weight but has 1/2" of z-axis play if you just push up on it gently. Is that normal?

What kind of screw?