I had two people leave my family sharing and I think I remember just removing the individuals. A new Family calendar was set up, but the old one was still there and still sharing with the two persons who were no longer part of family sharing. *sigh* I couldn't delete the old one and finally figured out that I, as the sharer, needed to stop sharing. Problem solved: I stopped sharing and then was able to delete the offending calendar. I just had to invite my three family members again and we are all good to go now.
Also, since I use an iPad and an iPhone, I noticed that even after choosing a default calendar on one of the devices, the other was still placing appointments in the old Family calendar. I checked the other device and the default calendar was not updated on it. I changed the default calendar on icloud.com, expecting that both devices would now show the same calendar, but not so. I had to manually change it. I suspect that signing out on the second device and signing back in would have solved the issue. Either way, I now have my problem completely solved.
Caveat:
We don't really use this feature and so have no shared events of any importance, just stuff that got put on there without me realizing it, frequently giving rise to the question about why was I sharing that event, which had absolutely nothing to do with them. I have no clue how this affects shared calendars that really serve a purpose.