Sounds like a personal decision. You pay into the system, and you should check with EDD to see if you are entitled to benefits. You earned those benefits through past work.
I don't know any employer who has ever asked whether an applicant has ever filed for unemployment benefits. I cannot imagine how an unemployment application would hurt you. Moreover, unemployment records are private and extremely difficult to obtain unless it is your case.
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There is no foreseeable downside to filing for benefits.
Neither one of your former employers will pay for your unemployment benefits directly, so I'm not sure what your concern is about how your former employers are involved. It sounds like your concerned about the amount you might get from unemployment, so here is information directly from the state website:
How are UI benefits calculated?
Benefits are calculated using an individual’s earnings during a specific 12 month period (this is called a base period). The base period begins approximately 15-17 months prior to the date the claim is filed. The amount paid each week is calculated based on the calendar quarter with the highest earnings during the base period.
If you have more concerns, check out the state website, which has a lot of helpful information about unemployment claims: http://www.edd.ca.gov/unemployment/FAQs.htm
This answer is provided for guidance only. DO NOT rely on it as legal advice. We DO NOT have an attorney-client relationship. You should contact an attorney in your area for a one-on-one consultation before pursuing any action or making any decisions.
This is in response to the additional information you posted below Ms. Slack's response. Unemployment benefits are taxable and must be reportes as gross income: http://www.irs.gov/taxtopics/tc418.html
Your eligibility for a credit card will be based on the card company's requirements. Being unemployed will probably hurt your eligibility for credit. Receiving unemployment should increase your income so may help you.
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