What happens to actions that are firing, then go outside the active time?

They stop firing, but can continue once in active time if you enable the 'Queue Until Active' flag on the Action's Advanced tab.

This flag puts delay on firing the action until it enters active time again. The 'Queue Until Active' flag description can be found in the Active Times section and is also explained in the manual as stated below:

The queueUntilActive setting controls what happens when an action which was triggered outside of an active time later re-enters that time (i.e. becomes active). If the action is still valid and this setting is set to true, then the action will then be fired and repeat / escalate as normal. Otherwise the action will remain un-fired until it is invalidated.