Can your iphone restore deleted pictures randomly?

If someone has inappropriate pictures on there phone, and thy blame it on "iCloud" and say they were old and deleted pictures and that they randomly restored back to there phone because of iCloud, is that possible?

Yes. Not just photos, but names (contacts) and other data. The thing is, it may not be from the iCloud. These things are 'backed up' all over the place in an effort to help you, the user, from losing anything, from losing data. The problem is, there are times when you WANT to lose data, but it is very hard to do as Apple and other apps try aggressively to 'help keep you' from losing data.

I have a contact on my phone that I can't get rid of. I desperately want to, but every time I delete her, she shows up the next day from somewhere, from some source as my phone continues to try to rebuild and restore what it believes is missing data.

I'm sure someone like Jennifer Lawrence would be more than happy to tell you how you should never trust anything to the iCloud.

NO, not by itself! There's a process you have to go through first! Picture will not just random appear back in your phone by themselves!