Doing Hajj-e-Badal for a person who has dementia
Q: Hajj was fard on a person, but he delayed it until he became old and lost his senses due to severe dementia. Is it valid for his family to fulfill the fard for him by:
1. Bringing him along for Hajj and making the intention of ihram etc for him
2. Doing hajj e-badal for him during his lifetime (note that he is not in his senses to command this, but it will be fully on their own initiative)
3. Doing hajj e-badal for him during after his death
Please provide the ruling for each of the three scenarios.