"○○の分まで" explanation

Japanese Language Grammar
1

I’ve seen the expression used in a couple of places and I’m not certain what it means.
I’ve seen it in phrases like these:
君の分まで僕は生きて往く。
ゆっくりわためPerson’s nameの分までねてくれよな。

2

I think it means to not only do your own share, but do the other person’s share of it, too.