Your understanding is not exactly accurate. A lender can not force you to payoff or refinance a loan due to the fact that you inherited a property. BUT, if you do not comply with the terms of the loan they can foreclose and take the property.
So if you can pay the past due amounts and bring the loan current then all you should have to do is make the payments according to the terms of the loan.
The problem is if you need to modify the terms of a loan and the note holder is deceased.
So if you can catch up on the arrears you may not have a problem, but if you need a loan modification or forebearance, that can be a problem.
“With respect to a real property loan secured by a lien on residential real property containing less than five dwelling units…a lender may not exercise its option pursuant to a due-on-sale clause upon—…(5) a transfer to a relative resulting from the death of a borrower;….”
Contact a real estate attorney for advice on your specific situation.