MY husband left me almost 2 years ago and may be living in his native Argentina. We were married in 1993 in the midwest but lived in California since 1994 till he left. Can I get a divorce on grounds of abandonment, and will I still be liable for all the debt he left behind? He is not a US citizent but he did have permanent resident status... I am struggling since he left.

You should or could have filed for divorce long ago. I doubt you have to have a "cause", but just merely file for divorce. Very few US states require you to even say why you want a divorce any longer.

Did you sign for the debts? Where are the debts, but you will need an attorney for the divorce since it is a little harder and will cost more since you don't know where he is