Don't write off that kid.
I teach part time and see this a lot. Especially from fellow teachers. Oh this kid has an alcoholic abusive dad, that kid has a mom with cancer, those 2 have family members in jail etc etc, followed by go easy on the struggling kid or this kid has no hope etc. If the kid flunks a test or skips class let it slide etc.
All this compounds the issue. What is required is the opposite of just sympathy.
Help them find their strengths and interests. Show them how to focus on positives and tune out negatives. Encourage whatever small steps you see them taking. Sensitize the other kids around them to be supportive. Show them examples of resilience and what it takes to be resilient. All these small things add up. Basically don't focus on the parent, focus on things you can do for the kid.
It's very hard to reprogram dysfunctional adults and get them to change, but kids are very different story. And there are few things more beautiful and satisfying, than watching a kid who has struggled for years and years, overcome and kick ass.