With a POA, would a daughter have to pay medical bills after her mother's death?

No you would not. POA is no longer in effect after death.

As Nance & Carol have said, POA's are only good while there are alive.

You do want to be careful to sign any & all documents as "Jane Smith as DPOA for Susan R. Smith" or "Susan R Smith as per Jane Smith, DPOA". If you just sign your name (Jane Smith), you could get billed for whatever is not paid by Medicare or Medicaid. This could become a real PIA to deal with.
Some states have filial responsibility laws on the books which can be used to try to make the children be responsible for their elderly parents care debt. By signing you are doing whatever as DPOA gets you out from that.

Debts die with them. But some states have it so that in probate, medical debts that are recent (30 -120 days prior to death) are to be paid from whatever assets are in the estate. But those medical debts (a claim) have to go to probate court system.

So if there is say 15K in hospital/physician debt after all insurance has paid and there is a home, then the 15K must be cleared/settled before the probate judge will release the property as per the will. I've been executrix twice and a lot of what I did was basically negotiate down debts for my aunts estates. If there are no true pressing concerns to close probate quickly, you can really push it and settle on 20-30% of what is owed or tell them they can go to court for their claim and you plan on taking 4 years (or whatever your states parameter is) to close the estate (you don't have to give a reason for this), so for 4 years they have to show up/file/whatever or they loose the entire claim.

No. Power of Attorney ceases with the death of the donor.

The executor or executrix of the estate would be responsible for paying from the estate assets. Though the POA document is void with the death of the person (except for decisions involving the proper care of the body) this could be the same person as the POA.

As far as those with survivorship on accounts and property, I am not totally sure how this all works, because it could put a hardship on a remaining spouse for instance. It definitely depends on state laws and I would consult an elder law attorney who could help if the bills are substantial.

Dear Kitty, No surviving relative/friend or associate is responsible for paying the bills of a deceased person. If there are funds in the estate, then the estate pays whatever it can, checks written by the executor.
My personal opinion is that funds from checking, savings, IRA's , 401K or 203 B's should go to the beneficiaries first, and then what's left should go to paying bills. There is also a very important concept called : trustee to trustee transfer. This has to be set up prior to the death of the loved one.....that way the creditors can't get their hands on any funds. They can threaten, of course, and they can even sue the estate, but so what. There'll be no funds in the estate after the transfer takes place.

I think I stated that the executor paid bills out of the estate funds not from personal sources. I have been an executrix and bills had to be paid first before settling the estate. You can set up things differently before the death occurs, but I was referring to after the death. It is possible to have to pay funds back to the estate in certain situations as my brother as learned.

In the case of someone with survivorship of accounts and property, this is usually considered non-probate and is not subject to the probate court even though it is usually listed on the probate appraisal.