New Mexico does have anti-deficiency laws; however, certain requirements must be met for a person to benefit from these laws.
In general, anti-deficiency laws only apply to primary mortgages on primary residential residences. Generally speaking, a primary residence is one where the person lives (as opposed to a house she might rent out or a property she purchased in order to “flip” and sell at a profit). A primary mortgage, generally, is the mortgage that you would take out in order to purchase your house (as opposed to a second mortgage that you might take out in order to raise capital.) Each state has its own requirements regarding when these laws apply. In Arizona, for example, the property must usually be 2.5 acres or less and be a one or two family dwelling.
Anti-deficiency laws protect people whose foreclosed homes sell for less than the amount of the outstanding debt on their mortgages by prohibiting the lender from collecting the remaining balance of the foreclosure. For example, if you owe your lender $300,000 on your mortgage but your house sells for $200,000 in a foreclosure sale, an anti-deficiency law will prohibit the lender from collecting the $100,000 remaining balance. By choosing to foreclose on your home, the lender cannot receive any money from you beyond what she can raise by selling that property.
Text of New Mexico’s anti-deficiency law (A.R.S. 33-729(A)) available at http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/33/00729.htm&Title=33&DocType=ARS