If you are not paying on either loan, each lender has the right to foreclose. In these trying economic times, the property is usually not worth what you owe on the first mortgage. Because the equity loan must in essence pay off the first mortgage in order to foreclose, it would end up worse off. If the first mortgage decides to foreclose, the equity loan would lose its rights to the real estate, but still have the right to sue you to recover the money it loaned. Bankruptcy would eliminate that right.
Depending on the value of the residence, you should consider a Chapter 13 bankruptcy. If the value of the house is less than the balance on the first mortgage, a Chapter 13 bankruptcy can eliminate the second mortgage and discharge any personal liability that you have.