Sure looks dangerous to me. With no support at the top it looks like hazard with seismic movement.
Was it built with that bend in it or has that occurred from damaged bricks below?
If you don’t remove it then at the least screw down some thick plywood in the attic underneath it all the way around so if you have an earthquake or if they decide to fall then the bricks won’t fall through the ceiling onto somebody. Top of the ceiling jousts or above the insulation if it’s thick. It would be best to have it removed though.
Looking at it you could remove it by hand without any tools.
Edit: added some info and replaced info I deleted by mistake.
At some point in time the chimney was abandoned. Most likely when the new roof was put on. New furnaces and water heaters can be vented out the side of the house with PVC pipe now.
I had a similar chimney and a year or two ago I had a new roof put on and I had them take the chimney down below the roof line like yours is and then while the hole was still open I took the rest down to the attic floor level and handed the bricks to the guys on the roof that tossed them to the ground.
You need to take that down to the floor level and cap it off.
It will be some work unless the attic has a window. You could rope off the area below and drop them one at a time, otherwise you need to get a 5 gallon bucket and carry them down and out a few at a time. the only other option I have seen people do is drop the bricks down the chimney one at a time and just leave them in there.
I would opt for taking them out and then repurpose the bricks into something else.
They will come apart easy all you will need is a claw hammer and maybe a old screwdriver. Just go slow until you get 6-7 rows off. There is a lot of weight there.
Mine is so much nicer now not having to work around it when I’m up there.
I would never suggest taking it down past the attic floor unless you were doing a gut job below. The little floor space you pick up isn’t worth it IMO.
It is likely plaster and lath covered in the living areas and sometimes they were structural for the first floor framing.
I use mine as a chase for my antenna wire to get to the basement and out the hole where the water heater used to vent.
IMO knocking a hole in the bottom could be kind of risky with that old construction and the weight above. If I were going to try it I would set up a video cam just in case and maybe win the 10k on American Funniest Videos.