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I have no experience with `dunst`, but generally you want a global service-level dropin file in `/etc/systemd/system/service.d/` with [`OnFailure=`](https://www.freedesktop.org/software/systemd/man/latest/systemd.unit.html#OnFailure=) setting in it. This way it gets added to all services running on your system. (Except to user units, you'll need to do this separately for those.) 

Then it's just a matter of writing  a failure notification (template) unit that interfaces with `dunst`. Mine evokes a small Haskell program which sends a desktop notification with [`libnotify`](https://wiki.archlinux.org/title/Desktop_notifications#Haskell).

You'll want to see this [ArchWiki section](https://wiki.archlinux.org/title/Systemd#Notifying_about_failed_services) about this. There's an important catch about stopping infinite recursion in the fabulous case where your notification unit itself fails.