In most cases there will be a will. That will should include an
executor and/or an attorney to deal with finalisation of all debts
of the estate before disbursement. Provided there are sufficient
assets, the attorney should be able to confirm acceptance of the
bill for the funeral costs.
In the first instance speak with the executor of the estate to
determine this.
Sadly, it may be that although the deceased has some assets,
occasionally there are far more debts to cover than assets can
provide. This presents a challenge for any other costs. However,
numerous countries and regions have laws in place to ensure that
the funeral cost is considered primary in settlement before other
debts.