Purchase money loans are non-recourse in California.

The non-judicial process of foreclosure is used when a power of sale clause exists in a mortgage or deed of trust. A "power of sale" clause is the clause in a deed of trust or mortgage, in which the borrower pre-authorizes the sale of property to pay off the balance on a loan in the event of their default. In deeds of trust or mortgages where a power of sale exists, as in California, the power given to the lender to sell the property may be executed by the lender or their representative, typically referred to as the trustee. This is uncommon in most other states where there is no "third party" that can execute the sale upon default by the borrower.

If the deed of trust or mortgage contains a power of sale clause and specifies the time, place and terms of sale, then the specified procedure must be followed. Otherwise, the non-judicial power of sale foreclosure is carried out by specific rules. Lenders may not seek a deficiency judgment after a non-judicial foreclosure sale and the borrower has no rights of redemption.

On the other hand, the judicial process of foreclosure, which involves filing a lawsuit to obtain a court order to foreclose, is used when no power of sale is present in the mortgage or deed of trust. This is uncommon with most commercially available real estate loans (i.e. Citi Mortgage) in CA and most likely would be found when there is a private party lending the money to purchase or finance the real property. Generally, once the court declares a foreclosure, the property will be auctioned off to the highest bidder. Using this type of foreclosure process, lenders may seek a deficiency judgement in an attempt to recoup some of their losses. Under certain circumstances, the borrower may have up to one (1) year to redeem the property.

As a rule, borrowers facing foreclosure and/or a short sale should consult their attorney and tax professional for expert advice.

Edit:

If as stated below, it was done subsequent to the purchase, your liability here is more complex, and depends in part on which lien forecloses first.

If the senior LH (Lien Holder) forecloses first, it will wipe out any junior LH. Should the proceeds on the senior lien's FC fail to cover the amount due on the HELOC, the lender can come after you for the difference, up until the statute of limitations on the debt has run.

The issue is whether the lender actually will do so. If you lack assets, it is unlikely they'll be interested in spending money to get a judgment.

The other important point here is to remember the "one action" rule. If the junior LH is the one who forecloses first, then you will not have personal liability on the junior lien (even on a HELOC) –
the junior LH will have taken its single bite of the apple by foreclosing, and takes only what its "bite" ends up producing. The senior LH, however, is still intact.

Some people, if they simply cannot pay both mortgages anymore, refi or a sale won't work, then they do what they can to keep the 1st TD current. Letting the HELOC go into arrears may force the HELOC lender to make a choice. This may force the HELOC lender to foreclose – and thereby eliminate your largest potential source of liability.

What happens after that is the concern of the junior LH, who has to then monitor the 1st TD to protect its interest in the property. You will, of course, then be evicted by the new record owner – the junior LH – who then gets to decide how to handle the senior LH (pay them off, bid at the senior's FC sale, etc.).

This is not advice, seek the advice of an attorney.