I've had thousands of spam emails sent with senders listed as nonexistent addresses from one of my domains. They were sent from third-party servers (my servers were not compromised and I had no open relays), and I only found out because of all the bouncebacks from naive receiving servers.
The only thing the domain holder can do at that point is to set up DomainKeys and similar measures - which still won't prevent spammers from using the domain, it'll just cause more of the mail to bounce back as spam.