If you have any further questions best contact attorney you dont want to loss your home.

I am surprised when you refi 1st loan did not pay off the 2nd loan, return mortgage broker ask about that surprised with refi if you could do this if behind on 2nd.

You will never be able sale the home till 2nd lien is paid in full.

Any lien can be foreclosed subject to the superior liens. So, the second lienholder can start a foreclosure proceeding that results in an auction. At that auction the buyer would receive the property with the first mortgage intact.

In your case if the second mortgage company foreclosed and nobody bought it at auction, they would wind up owning it with your $436k mortgage attached. Most second lienholders don't want that. The Due on Sale clause could then be activated by the first lienholder and they could demand immediate payment of the $436k.

So, technically yes they can. Would they? Only idiots would, but there seems to be an incurable strain of that running around these days. Be careful they don't infect you with it.
Try talking to them. Again and again. Of course, they are going to ask why the $480 a month they collect is so difficult since you're paying over $2,000 on your first. You just knocked that down from $3,000 so you should have it from the savings on your first loan mod.

I believe they can and take posession of the home.