Look at the article, what I am suggesting is not a lien strip, it is discharging the second mortgage in a chapter 7, what that would do is discharge any personal liability you have on the loan, and they can only foreclose on you, but if they do the first would be paid and they would receive nothing.
In most cases the second will not bother with a foreclosure as they do not receive anything.
Typically on first mortgages if you discharge the first, you can live in the home, by paying the monthly payments.
In a second that is under water, you can also pay the monthly amount, or in your case if you do not pay the monthly amount, they can either foreclose, or settle with you for some small amount. They cannot foreclose, without the first being paid, or being notified.
In a chapter 13, you can lien strip the second, and they cannot foreclose on you as their secured interest is gone.