What do you do if your ex wants to declare bankruptcy?

Answer

Check your divorce paperwork. Usually, there's a provision within the decree stating that any financial obligations- such as alimony or child support- are still valid claims when a bankruptcy is declared. If your lawyer didn't do his/her homework and there is no such provision, you stand in line with the ex's other creditors.  

Answer

I am not giving legal advice and nothing in this posting should be construed to be legal advice, but it is my understanding that when one ex-spouse files bankruptcy on a mortgage, the mortgage lender usually doesn't care so long as the other ex-spouse maintains payments. This doesn't mean that your particular mortgage lender will agree. Please understand that I am not suggesting any course or action or inaction, I am simply relating what my understanding is, which may or may not be accurate in your jurisdiction
I don't think there is much you can do except give your ex morale support as they are not legally tied to you so therefore you are not responsible for any debts that your ex has accumulated ever since the break up.