I have gotten a few extra pics from villagers. In my experience it has just been the same as getting their pic the first time around (complete request and receive it as a thank-you gift) I didn't do anything special, it just happened. I have also received a second pic from villagers who have already given me theirs but then moved away and given me a second one as an attachment to their 'goodbye' letter. Hope this answers you're question!
EDIT: uh... this was supposed to a reply to D I A's comment. I'm new to the forum and I have no idea what i'm doing.