The lender is foreclosing on the whoever owns the property and hasn't paid the mortgage, which I guess is your trust, assuming you were the one on the Note and you had the right to transfer the property to your trust.
Other alternatives to foreclosure include loan modification, short sale, and deed in lieu - have you considered those? See a real estate lawyer to review your loan documents for specific advice.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
If the property is properly titled, the legal title is in the name of the trustees of the trust. But whoever has title is responsible to make the Deed of Trust (DOT) payments or the trustee of the DOT can exercise the power of sale granted in the DOT. These powers were granted by the legal title holder at the time the loan was granted/funded and remain with the property until repaid is some manner. This process is a non-judicial foreclosure under CC2924.
Good news is that if you owe more than the property is worth and this is your primary residence, the noteholder can not sue you for the difference....thanks to California's anti-deficiency laws....CCP580(b) or (d).