Legal Question in Employment Law in California

A California employer does not have to pay an employee sick leave (or, for that matter, vacation time). If an employer chooses to do so, the employer may set the terms for accruing sick leave - such as requiring that an employee work a certain number of hours in a week.

By the way, you may be eligible for partial unemployment benefits if you decide to keep working for this employer. Here is a website explaining California Emplooyment Development Department's (EDD) worksharing program: http://www.edd.ca.gov/pdf_pub_ctr/de8714bb.pdf. You may want to discuss this with your employer.