I don’t know of any plugins that will allow for this.
Are you users required to log into the site when registering at all or is the event completely open to the public?
Have you confirmed that these users requesting copies actually received the original email? The problem may well be that they didn’t receive the initial email to begin with and if that is the case, fixing that would reduce this somewhat.
The closest we have for this is the ESPRESSO_MY_EVENTS shortcode for the WP user integration add-on, however, it requires you had that add-on activated during the registration and that our users need to log into the site, see: