As of February 18, 2021, the “Unknown Repository” issue has been resolved. You should be ok to delete repositories once all the branches have been merged.
Deleting forked repositories will erase history from your Pull Requests.
Deleting a forked repository will delete any information associated with your repository. This can retroactively affect any references to your repository, including pull requests that have already been merged. (See Pull request displays "unknown repo" after deletion of fork)
Your comments and commits should be preserved on any pull requests that were associated with your repository, but you will do so at your own risk.
However, deleting old branches after a merge is perfectly safe.
While deleting repositories should be avoided, deleting unused branches is perfectly acceptable. In fact, GitHub encourages you to delete old branches.
Tidying up after Pull Requests
At GitHub, we love to use Pull Requests all day, every day. The only trouble is that we end up with a lot of defunct branches after Pull Requests have been merged or closed. From time to time, one of us would clear out these branches with a script, but we thought it would be better to take care of this step as part of our regular workflow on GitHub.com.
Starting today, after a Pull Request has been merged, you’ll see a button to delete the lingering branch:
If the Pull Request was closed without being merged, the button will look a little different to warn you about deleting unmerged commits:
Of course, you can only delete branches in repositories that you have push access to.
Enjoy your tidy repositories!
Alternatively, if you really don't want to keep them around, you can archive a repository to indicate it is no longer actively maintained.