In California, an individual who files for unemployment insurance benefits must meet specific eligibility requirements before benefits can be paid. The reason an individual is out of work can affect his/her eligibility for benefits.
The eligibility requirements include being unemployed through no fault of his/her own.
A person who quits work or is fired from work will be scheduled to a telephone interview because there is a "separation issue" that must be resolved. The EDD interviewer obtains and documents information about the separation from the employer and claimant and decides, according to law and regulations, if the person is eligible to collect benefits. The EDD mails a notice to the claimant who is not eligible for benefits.
The EDD also mails a notice to the employer who responded timely to the notice of claim filed. The notice advises the employer about whether the claimant is eligible or not, and whether the employer's account will be charged for benefits paid to the former employee.
Either party can disagree with an unfavorable decision and file an appeal.
Quitting a job due to stress will probably not be sufficient to qualify for unemployment benefits. You will probably need to provide more tangible evidence to support the necessity of the decision, such as medical documentation from a doctor diagnosing a condition which, if not alleviated by leaving the employer, may pose a real risk of serious harm to you.
I suggest you go to the benefit determination guide on the EDD website to familiarize yourself with how the EDD views issues relating to employees who voluntarily quit their jobs. You can find it at http://www.edd.ca.gov/UIBDG/Voluntary_Quit_-_Table_of_Contents.htm .
Generally, a person who voluntarily quits/resigns is not eligible for unemployment benefits unless "good cause" exists for such resignation. There is no bright line test for what constitutes "good cause," however medical condition is one of such causes if it is sufficiently severe. If you resign, be ready to explain to the administrative law judge why exactly you resigned, what specifically was so unbearable at work and whether you made any efforts to resolve the situation. Generally, it's an uphill battle, but having specific, compelling arguments, such as your exact diagnosis, doctor's orders to stay away from workplace, etc... will be helpful.