Well one way spammers can take advantage of a server is through outdated scripts. Like php scripts for example. If they are outdated that most likely means they are unsecure which means if they are not updated on the server even in a shared hosting environment your server is at risk of being hacked by a hacker that just wants to do damage or by a spam hacker.

They will hack in to your account through the script and then place scripts of there own that attach them self to send mail and send spam and you think it is the account that is doing it. If your server has many unsecure or outdated scripts on it they can just move from account to account and make it really hard to track or stop.