There is no appeal for hardship. Verify from the timeline that she was in F-1 status on the recognized filing date. If she was, consult with an attorney.
The sooner she attends to it the better. ICE/DHS could be alerted by the university. It is easiest to just get stamping and reenter. If she has H-4 stamping, she just needs to exit and reenter to regain that status; if not, she must appear for H-4 stamping.
It may, but issues with finances and non-immigrant intent proof as required for F-1 visa are more likely to be a problem for F-1 stamping. Remember there are rules for entry on F-1 before beginning of the program.

