Catch-all feature?

Is there any way to implement an catch-all feature to redirect any inbound links that are currently not known to a custom 404 page while logging them so you can go back to them and add them to the redirect list? I figure it’s better to have a soft 404 error that lets you know that it has occurred so you can monitor that to add to the master list. Does this currently exist?

https://wordpress.org/plugins/redirection/