Nearly every funeral is eventually paid for out of what the person left. Hardly any is paid for out of it on the day. A bank freezes an account when it learns of a death, probate takes months where there is any at all, and the funeral happens in the first week. That gap is the practical problem, and it catches families who are not short of money in the slightest.
The usual bridge is a life insurance policy. Most insurers will allow one to be assigned: the claim is paid to the funeral home directly, up to the amount of the bill, and whatever is left goes to the beneficiary as it would have done anyway. A family then does not have to find the money and wait to be repaid. Whether an insurer will do it, and how quickly, varies enormously — so bring the policy to the arrangement meeting rather than mentioning it afterwards. That is the difference between assigning a policy and lending your own money to an estate.
Where there is no policy, somebody usually pays and reclaims from the estate later. Whoever that is should keep every receipt, and should get advice from somebody qualified to give it about how funeral expenses rank against everything else the estate owes. We will not guess at that, and you should be wary of any funeral director who does.