Legal Question in Real Estate Law in California

I think you mean if the lender forecloses, can the bank require you to pay that money.

Answering your question requires detailed answers to several questions. If the property is only subject to one deed of trust, and the lender forecloses, the lender cannot get a deficiency judgment pursuant to Code of Civil Procedure section 580d. If the lender forecloses by way of lawsuit, known as judicial foreclosure, the lender is prohibited from obtaining a deficiency judgment if the purchase money deficiency prohibition of Code of Civil Procedure section 580b applies. I cannot tell whether this applies from the limited facts in your post.

A cosignor is just another name for a guarantor. Normally a guarantor is additional security. A foreclosure by trustee's sale would prevent a lawsuit against a guarantor, unless the cosignor signed what is commonly known as a "Gradsky" waiver. Again, I would have to look at the underlying paperwork and ask you several questions to give you a definitive answer.