When enabling the Epic support for Scrum Board, we will get a panel listing all of the Epic associated to the board. And with this, we can drag and drop issues listed in Backlog to Epics as needed.

However, if all issues mapped to the Epic is already completed, and the Epic itself is closed in JIRA, apparently the Epic will still listed in the board. And furthermore, we are still able to drag and drop issues to a closed Epic.

Sample screenshot illustrating the behavior:

This may cause some confusion when using the Scrum board, hence it will be great if Closed Epics are removed from the Scrum board.