OK so this is what it looks like:
####
## ##
# #
# ##<--F#X
# # DDF#X
# #
## ##
####
Key: XX = stairs, ### = pit walls, F = floor, D = what I'm trying to dig through
I found a deep pit feature linking two caverns vertically. There's this weird tall column of rock or you might call it a stalagmite (not a stalactite) in the center of the pit. It looked like an awesome place for a stairway. So I've dug stairs halfway down the walls of the pit to reach the fat stalagmite, and I'm trying to get across some open space in the direction of the arrow in the picture. I'm also trying to dig through walls of a thinner stalagmite marked D in the picture, that's in my way, but my miners keep dying in cave-ins. Yet after each time, the site looks the same as before, but caves in again the next time I dig the...
Oh, shit.
I just realized where the cave-ins are coming from: when I try to tunnel through the small stalagmite to get to the bigger one, the "nose cone" of the thin stalagmite is unsupported, and the whole thing drops one Z-level and squishes the miner inside. After the dust clears, everything looks the same as before (because the tip of the thin stalagmite is lowered but still many stories above). Then I try to mine out the thin stalagmite again, and it drops another Z-level, and so on.
Well! Glad we cleared that up: clearly all I have to do is keep doing the same thing, and eventually the thin stalagmite will be completely gone!