How does the government decide who will be a care provider?

Let’s say that there is a brother age 19 and a sister age 23. The parents of the two are aging and getting close to 60. The sister has had a history of mental issues and have been diagnosed to have a chemical imbalance in her brain. God-forbid anything happening to the parents because the mother have devoted most of her time to the daughter to care for her ever since the diagnosis.

Does the Government require the most direct family member to care for a person with mental issues if the parents can no longer do so?

If yes in this case would the brother have to care for the sister even though he technically is just getting his life started and has no stable source of income etc. etc.