Hello Aaron. I am sorry to hear that you are in this unfortunate situation. I'll answer your questions in the order in which the appear in your post.
A trustee sale is essentially an auction at the court house and it's the final step of the foreclosure procedure. In CA, real estate loans are typically secured by a deed of trust and the borrower is known as the trustor. The trustee is holding title to the property for the lender and the deed of trust gives the trustee the authority to foreclose on the property without having to seek a court judgment when the borrower/trustor defaults on the loan payment. The CA foreclosure process starts with a notice of default and ends with the trustee sale.
Effective July 8, 2008, a tenant or subtenant in possession of a rental housing unit that has been sold through foreclosure is generally entitled to a 60-day written notice to quit. However, a borrower who remains on the property after foreclosure may be served a three-day notice to terminate. This law does not affect, among other things, rent-controlled properties with just-cause evictions. Effective September 8, 2008, the lender, trustee, or authorized agent posting a notice of sale must also post and mail a specified notice of a tenantâ€™s right to a 60-day eviction notice from the new owner, unless other laws apply. This requirement to notify tenants of their rights applies to loans secured by residential real property where the borrower has a different billing address than the property address.
It is possible that the lender would prefer not having to go through the eviction process and it is also possible that you would not want to have an eviction on your record. The lender may very well be willing to offer you cash in exchange of you agreeing to voluntarily vacate the property by a certain day. Typically, they don't offer more than $1,500, but now that they have to give you at least 60 days notice, they may be willing to offer more as it would be beneficial to them if they could get the property on the market sooner. In the current market, the property values can easily drop 1 or 2% in 60 days and it would be cheaper for the bank to get the property on the market now than in 2 months. Anyway, that's just me thinking logically, but unfortunately banks don't seem to always make rationale decisions.
It's ironic that you as a tenant can stay in the house longer than your landlord (in theory anyway).
Good luck to you.