Thank you for the oppoirutnity to assist you.
Q) Should I pick it up?
Don't pick up either. Just get your real ID replaced. The fake ID is illegal; if you go to retrieve it, you're asking for trouble and you'll probably be arrested. Get a new phone case, and chalk this up to an expensive lesson.
If the police or campus security want to question you about the the fake ID, whether it was yours, why it was in your phone case, etc., SAY NOTHING. Do NOT answer any questions or make any statements about ANYTHING. Just say, "I want to speak to an attorney" no matter what they say. If you do answer their questions or try to explain what happened, it's likely you'll simply be charged with a crime. You might be charged anyway, but don't HELP the police to take out charges against you.
I hope my response has been helpful. If you have follow-up questions or concerns on this topic, please ask. I'll get back to you as quickly as I can, although I may not be online at the moment you respond. Otherwise, I hope you will rate my answer positively as that is the ONLY way I receive credit for my work, and doing so will NOT cost you an additional fee.
Best wishes to you,