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