Emotionally speaking, I think it's important to remember that Chris has already experienced the loss of a parent - it won't be a step into completely unknown territory for him. He won't go nuts, he won't start painting Sonichu amiibos with his own feces and selling them on Etsy. He will grieve, just like we all would, and I don't expect that the grieving process will be exceptionally different for Chris than it is for anyone else. He isn't emotionally reliant upon Barb in the weird fuckmommy way that is occasionally implied here - in fact, with his regular attendance at Impulse, he's showing significant emotional independence. He's going out on his own and attempting to find a new social group independent of his mother, and moreover, one that she would probably disapprove of quite strongly.
Practically speaking, there's something that several posts in this thread have completely overlooked: Barb is far more reliant upon Chris than Chris is upon Barb. Even though we don't know the details of daily life in the household, from what we do know it's pretty obvious that Chris can care for himself on a day-to-day basis. He is perfectly capable of going to the shops, paying his bills, and so on. Barb is much less capable - whether due to laziness, infirmity, or some combination of the two, she isn't the one who runs the household. When Barb dies, it may actually significantly unburden Chris.
He'll have to catch up quite quickly on things like property taxes, home insurance (hah!), and so on, but I doubt that's beyond his capacity.
Lastly, and quite speculatively, I think it'd be interesting if once Barb dies, Chris ditched the Hoard, sold 14BLC, and moved into Charlottesville. He obviously wouldn't be able to afford a house, but I expect he'd be able to find an apartment that was within his means. That could do him a world of good.