If your loan is in trouble, it's time to find a lawyer. First money purchases (the first loan you sign up for) in MANY states are non-recourse. This means the bank can't do a thing if you don't pay (though they may try to convince you otherwise)
Once you refinance, you are now on the hook for your loan amount, and they can come after your assets and after your wages.
Under conventional financing terms loan-to-value (LTV) ratios over 80% have required what is called "PMI" - private mortgage insurance. The purpose of this is to guarantee for the lender that they can recover if you don't pay and, post-foreclosure, your home isn't worth enough to satisfy the mortgage.
One of the reasons for this requirement is that in most states purchase money first mortgages are non-recourse. That is, if you default they can take the house and ruin your credit - but it ends there. In those states they cannot pursue you beyond foreclosure and reclamation of the house.
In every state if you refinance the resulting mortgage is a recourse loan, which means they can sue you for any deficiency if you subsequently default and come after any other assets (other than retirement funds - which is why you NEVER EVER raid a 401k or IRA to stay afloat!) and even try to get a wage garnishment - and they just might!
For this and other reasons nobody should ever refinance a mortgage that is in trouble without getting qualfiied legal and accounting advice. It could be the cheapest $500 you ever spend.