I wouldn't be concerned about your HELOC (Home Equity Line Of Credit) bringing an action of foreclosure against you, as they are 2nd position lien holder. If they are competent in the least, they will file for a money judgment, which will still attach to the property in New York State automatically, and then they will have the ability to seek an income execution and potentially pursue your wages and/or bank accounts.
You should contact a local bankruptcy/debt relief attorney as soon as possible before any action begins so that you have the maximum amount of time to plan your strategy moving forward.
If the value of your home is less that the payoff of your primary mortgage alone, through a chapter 13 bankruptcy petition you can move the court to remove the HELOC completely, and possibly modify your primary mortgage at the same time. Start with a CMA (Comparative Market Analysis) from a local realtor, or a BPO (Broker's Pricing Opinion) from a local real estate broker (should be free, don't let anyone charge you, they are very easy to do) so you can show your attorney and they can give you the best possible legal advice. Then you can make an informed decision on how you want to move forward.