The answer could be yes or no depending on what you did in probate. Presumably you had a lawyer for probate (it can be an expensive mistake to wing it), so you need to call the attorney who handled the probate and discuss the details.

The HOA can file a claim with your father's estate. They cannot pursue the heirs directly. However, land usually passes outside a will, so the heirs would have owned the property as of the date of death.

If the property was mortgaged, the heirs (if there was no will) or the named beneficiaries who got the property (if there was a will) were responsible for the mortgage and HOA payments. Why wasn't this done? Was an attempt made to sell the property?

And was an estate ever probated for your father? If not, then if there is a will, the person named as the personal representative should go to a probate attorney immediately in the county/state where your father lived at the time of his death. If there is no will, then I recommend that the heirs decide who lived closest to your father and who is best suited to wrap up his affairs and make that person the personal representative.

If this was in probate, then it really is not ethical for me to discuss the legal issues with your father's estate. It has an attorney and you need to direct your questions there. If you are not the named personal representative, you need to talk to the personal representative to find out what has happened and why the dues and mortgage were not paid.

Allowing the house to go in foreclosure and not payiong the HOA are not a good idea, but then it will depend on what assets there are in your father's estate, whether his property was a part of the estate and how all this happened. You do not address these facts and the answer will depend on how these questions are resolved.