Employees file for unemployment all the time when they may or may not be eligible. There is a whole appeal process which takes a look at who is really the "moving party" when an employee leaves.

> Frequently after notice of a quit, layoff, or discharge has been given, either the claimant or the employer will act to accelerate the separation. Such action can alter the character of the separation.

https://www.edd.ca.gov/uibdg/Voluntary_Quit_VQ_135.htm

I don't really think unemployment is relevant in this case. I am interested in whether she technically quit or resigned though.