BF wrote:
I have an old wood fence that finally died in the usual fashion -- the
posts rotted at the base and broke. Part of the fence is on concrete
slab, and I was wondering if it is possible to extract the broken-off
part of the posts from the existing post holes, and set the new posts
in the same holes? Or will I need to do some demolition work on the
slab and set the new posts in new concrete?

Thanks for any advice,
Rick

There is no good way of doing this.

BTW, while it depends on the area, it may be better and result in longer
lasting post to not use concrete and put the post directly in the ground.
Concrete sometimes traps more moisture and caused post rot.

--
Joseph Meehan

26 + 6 = 1 It's Irish Math