Undeliverable emails not coming back through distribution group

Hi everyone

Is it possible to have undeliverable emails go back to a distribution group and then to the members of that group?

We use a ticketing system here and have a distribution group called support@domain.ca.  If I sent mail from this address to a non-existent address, I see on the Exchange server it failed, but no undeliverable message was returned to us.

Maybe this makes sense and there's a reason I'm unaware of for this not to work.

Thanks

Ryan