It is the right thing to do in the most general sense but that oversimplifies it. Just because it the right thing does that mean everyone should feel responsible to do it? What if they can't? What if their parents were abusive? What if someone else is taking care of them? What if they are no longer connected to you? What if they were abusive but have changed for the better? What if they were good people/parents but aren't anymore? I think it comes down if it need from and if you can emotionally, financially, physically and/or whatever necessary to take care of them and yourself. If it too much of an emotional burden then don't feel responsible. The same if its too much of an financial, mental, and/or etc burden.
Ok, with all that being said, just remember everyone has reasons for doing what they do? That doesn't mean you have to trust or accept them, but please don't be to harsh on a bad person especially if they are trying to change.
Also I believe God has a plan of happiness for all of us because he loves us all. Part of that plan if the agency to choose what to do, even including being horrible people or amazing people. It also includes trials and tribulation, and has accounted for satan's interference.
Those were some of my thoughts, including the ones I thought were most important.