Can’t speak for an airliner parachute system that doesn’t exist, but in small airplanes where such parachutes do exist…
While airborne, if the 'chute deploys one of two things will generally happen:
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If the system deploys at too high a speed then stuff comes apart. And by “come apart” I mean bits and pieces depart the airplane. There have been accounts of things like engines being ripped loose, the airframe being wrenched out of shape to the point the controls don’t work anymore, and so forth. Basically, if your airplane wasn’t wrecked already it is now and you plummet to the ground with absolutely no control whatsoever.
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the cables holding the chute to the airplane snap and the parachute goes sailing off without out the chute - but probably not before it slows the aircraft down so much that it is no longer flying and you plummet to the ground with absolutely no control whatsoever.
The above two reasons are why the manuals for such airframe parachutes (and yes, I have actually read such manuals) are pretty adamant that if you have control of the airplane at all and the opportunity for a controlled landing continue to fly the airplane rather than pull the Big Red Handle (yes, they really are red) is your best option. Such parachutes are ONLY for when there is no other choice. “Engine failure”, by the way, is not sufficient reason to pull the handle - as has been demonstrated, it is possible to land an unpowered airliner on a river and still have everyone survive. Situations where it makes sense to use a parachute are extreme and fortunately very rare.
I’ll also point out that these parachutes are intended to give you a chance to survive - a gentle landing is in no way guaranteed. You may still wind up with spinal injuries, broken bones, concussions, etc. It is NOT a pleasant experience base on talking to people who have actually taken that ride. Beats dying, and most of the injuries are the sort you’ll eventually recover from, but multiple broken bones are no fun at all. If you land in a body of water or power lines or something of the sort you might survive the fall but not the landing after all - really sucks to survive a plane crash then drown.
Parachutes accidentally deploying on the ground are frickin’ dangerous - they are launched by solid fuel rocket to get them out and opening as rapidly as possible. If these things go off on the ground they go through things, like walls, other aircraft/vehicles, and people. In fact, it was after one two many instances of someone on the ground being skewered by one of these things going off when they shouldn’t that the UK banned airframe parachutes.
So, although such parachutes really have saved some lives and can be extremely valuable, they are not without hazards themselves.