How do family members resolve how best to care for elderly parents with dementia, loss of mobility and limited amount of finances?

Are both parents in the same boat? Does someone have POA? Are they still living together at home? Who gets a say in how to resolve the situation?

Agree with Alva's questions. Would be helpful for you to provide more specific info.

This depends on the family. Each case is individual.
What is your particular family dealing with? How many members are involved? Are there disagreements right now and what are they?