A parent that you care for can qualify as your dependent.
Your parent would not be considered your "Qualifying Child" but if you meet the requirements, your parent would be considered your "Qualifying Relative" in which case you would claim your parent as a dependent and receive your parent's exemption.
Your parent can still file as well, if they thought they might be due a refund, but they would choose "Someone else can claim me" which would allow you to take the exemption.
Here are some of the requirements to claim a dependent:
Do they live with you? Usually our relative must live at your residence all year or be on the list of “relatives who do not live with you”. Parents are on that list and do not have to live with you as long as you pay more than half of their support.
- Do they make less than $4,050 in 2016? Your relative cannot have a gross income of more than $4,050 in 2016 and be claimed by you as a dependent.
- Do you financially support them? You must provide more than half of your relative’s total support each year.
- Are you the only person claiming them? This means you can’t claim the same person twice, once as a qualifying relative and again as a qualifying child. It also means you can’t claim a relative—say a cousin—if someone else, such as his parents, also claim him.
If you answered yes to all, and:
- your parent is a citizen or resident
- you are the only person claiming you parent
- your parent is not filing a joint return
Here is a link to more useful information: