Can a family member take out a loan under their elderly father's name if they Power of Attorney?

That would depend on what it is for and why you (he) wants it. I think this would be very hard. You may want to check with an elder law attorney about this, but from what I know it wouldn't be likely.
Carol

The Durable Power of Attorney is extremely powerful and if the person who has it is very smart and wants to abuse it they can. They can manipulate an elder very easily.

My sister had Durable Power of Attorney and now mom's house has a mortgage. I am hiring counsel to find out how that got done behind my back (I am on the house title) and how mom's Will got me, her caretaker and only daughter within 2000 miles, cut out of her will.

Mom rescinded her power and now I have it and the will was voided.

Yes they can if it specifically states that they can take out loans in their name.