What’s the deal with alternative transportation when JR is stopped?

As the title says, alternative transportation on JR commuter pass when the trains are stopped, specifically, why are certain lines on my route home sometimes covered and sometimes not? Where I live there are 2 stations, JR and another, sometimes the alternative transportation is allowed all the way home, but other times I am responsible for the last ¥500.

Edit: I'm really not understanding why this is being downvoted.