

I would think that any object (including the ship) is traveling at a sub-light speed within the warp bubble and therefore would only keep that same velocity when (catastrophically) exiting the warp bubble. Unless by exiting the warp bubble in an uncontrolled manner creates some other force which slows the object somehow.
My understanding is that the warp bubble is moving space around the object (including the ship) rather than accelerating the object to FTL (faster-than-light) speeds, thus we really only have to consider the relative velocities within the warp bubble.
Edit to add: Oh, also, I should add that (IMO) the object cannot continue to travel at FTL speed since it has no warp drive of its own to maintain the warp field.
It’s also possible that “Nova Squadron” is just one of many (as Value Subtracted mentions herein) and that there are many other Nova Squadrons without any issues in the intermittent years between the incidents. It’s possible that, like most things in the Star Trek universe, we only see the times when something interesting/dramatic occurs, not the boring day-to-day.
Said another way, just because you periodically have a rowdy graduating class from primary/secondary education, doesn’t mean you stop having graduating students.