I'm wondering how you/they know its unsupported. Normally you'd have to
rip out some ceiling or floorboards to even get to look at whats going
on. Since the floorboards are there, is the house in such a state that
the necessary ceiling is missing? If not, the surveyor might have
misidentified the idiot.

What you do is go down the cellar and look at where the hearth was.
When you so it isn't that's when you know.

(Unless the idiots stripped out the floor and inserted lots and lots of
expensive ironmongery so they could have more room in the cellar.)

I would imagine that after having tons and tons of masonry cleing to
the gable wall there will be a fair bit of distortion. If you can't see
it and there are no cracks in it then it might be possible to repair it
for 10 or 15 thousand. (To take down the stack. I don't know if putting
the base back will be safe enough.)

When it collapses it will drop instantly and give little or no warning,
so the house will be uninhabitable untill all the chimney is removed or
reinstated.

I wouldn't bother. And it aught to be illegal to pass on dangerous
property like that whether or not the customer has been advised of it.

It shouldn't cost 10k to remove a stack!! (Unless the house is huge
with more than 2 stacks. Ive removed a single stack in a kitchen for
less than 2k.