What would happen if the bicycle saddle was too loose?

Depends on what it is that's too loose. If the saddle is properly attached to the seat post, and it's the seat post that's not sufficiently attached to the bike frame - then the saddle will simply end up lower against the frame as time goes by. Or it can start going sideways.

If it's the saddle that isn't clamped sufficiently to the seat post, then it can be bad. It can tilt either nose up or nose down, which can be either uncomfortable or outright dangerous if you're coming off a jump. Worst case is the saddle coming off the post entirely, which would put the rider at great risk of injury.