Hello, Can I claim a distant relative of mine who stays with me at least more than half a year, receives his mail at my address but he also receives general relief ...?

It depends. You can check the qualifying persons rules in the IRS Publication 501.

You can claim a child, relative, friend, fiance (etc.) as a dependent on your 2016 taxes as long as they meet all of the following requirements :

• You provided more than half of their financial support. More info
• They made less than $4,050 in gross income during 2016 unless they are a qualifying child.
• They live with you or they are related to you.
• They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren't (or won't be) claimed as a dependent by someone else.
• They aren’t filing a joint return with their spouse.
• You are not being claimed as a dependent on someone else's return.

It's OK if you're still not sure about your dependent situation. TurboTax will ask you all the right questions to figure out all your dependent details.

If you are looking for information on a qualifying relative for head of household purposes please see the following FAQ article. 

https://ttlc.intuit.com/replies/4791157