looks to be a mycedium, a type of chalice...however it appears to be a formerly unhappy chalice, the skeletal structure appears to be old, if it was fresh tissue loss, it should be all white...might be just fine.
I agree. It's definitely a Mycedium sp. either M. mancaoi or M. elephatotus. The tissue recession does seem to be old. Just give it moderate light and low, feed it a couple times a week and it'll be growing like crazy.
although hard to tell for sure my guess would be some kind of oxypora.
Mycedium have the trait that all coralites are orientated towards the perimeter and although you can't be 100% because it is a small piece the coralites appear to be orientated upward .