Sorry to hear about your situation.
The first two answers are as good as you are going to get on a public forum such as this, where the professionals answering are not attorneys. You are asking a legal question of non-legal people. We are restricted to "Yep, they might negotiate or they might foreclose..."
I recommend you contact Kristi Collins of The Scottsdale Law Group and ask for a consultation. They specialize in this type of situation and help people all over Arizona. Only then will you have an idea of your best course of action. You can reach her at: email@example.com or (480) 478-0709.
Who is your bank? Some banks are settling 2nd liens. I know that because I am in touch with some executives at one of the largest lenders in the USA. In your case, your combined loan to value is over 100% so most probably they will not proceed on foreclosing your 2nd lien. Did you try to talk to your bank about either settling your second loan or applying for a 2nd lien loan modification? If not, you should try doing so. Also MyCaal.com has the best platform for applying to a loan modification shall you decide to make lower payments and if you are not successful at settling it.