Normally such places are only used in one record. If you are looking at the place record, use the "Referenced By" menu command to find the record and delete in the place field first. You can then delete the place record. If you are cleaning up a file, you can work with the place fields and remove all unlinked place records later by searching for them (see search window and record type of unused place).
This situtation didn't arise in my place editing. Normally I was changing place names, but never deleting them. I will try to think of better way handle place record deletions when they are still used in place fields.