Is it legal to take POA after a stroke with dementia?

I'm moving your question to the top. Hopefully, people with answers will see it.

I think the issue turns on whether the person had dementia prior to the stroke, what the effect of the stroke was in terms of cognition, and whether that person can still make decisions for him or herself. Unfortunately, it's not always a" clear cut" situation.

I agree, I’ve just done a POA for my aging parents. My mom had a stroke, but is still considered by her medical provider to be of sound enough mind to make her own decisions. If POA cannot be taken, many states have a form of legal guardianship that you might want to check into. Hope this helps.

It depends on how your POA is written. Does your love one have to be fully compentent. In state of MI, the POA, I have states the person has to deemed "incompentent" prior to exercising the "full" legal POA. Good luck with getting a doctor and psychiatrist to 'legally sign off on that", since as long as your loved one can count to 10, and know who the president is of the United States your out of luck. However, I do manage some finances and health decisions for my mom. HOWEVER, she can "trump" any of my decisions since she is not deemed "incompent" and she knows that. Example, a recent hospital visit, due to a fall, upon discharge, advise hospital she lives alone and they deemed her as 'unsafe' going home by herself and recommended rehab 1st for a couple of weeks. She REFUSED the outsource living rehab. Previous hospital visits, (there has been a least one a year for almost 5 years) the health care professionals were able to convince her to go to a living rehab facility for a couple of weeks. She is very stubborn, and angry these days with me, which keeps her going and will make "un-safe" decisions. Her safety and health judgements is OFF. With all that said, about one year ago we established an Irrevocable Trust, since having issues with 'greedy' family members as well.
Be proactive, get a trust & full guardianship, if your love one agrees.
Good luck to you and your loved one