Durable power of attorney and medical power of attorney are valuable to control decision making when a person is alive, but it ends at the moment of death.
The number one thing to do is have a will that spells out clearly what your wishes are. Even with a will, once it goes into probate after death the law clearly spells out which expenses get paid first out of the estate and then any money or property remaining gets distributed to the beneficiaries as per the directives in the will. The expense payments go in the following order:
1. Funeral expenses
2. Expenses related to the execution of the estate (legal and administrative fees)
3. Medical expenses unpaid in last 6 months
4. Creditors (most bills including credit cards, loans, utilities, etc.)
5. Medical expenses unpaid prior to the last 6 months
6. All other legal claimants
If there is no will, then the remaining estate goes in solely to the next of kin in the following order:
1. Surviving spouse
2. Surviving children
3. Surviving parents
4. Surviving siblings
5. State commonwealth for petition by any remaining relatives
There are hundreds of other details but one that is most important is that a full inventory must be taken and valued before any distributions to expenses or beneficiaries are permitted with the exception of money to pay for the funeral expenses.
In other words, no taking moms old desk lamp until it is legally given to you.