What’s at the far (upper) end of a Jeffries tube?

I think it depends on the specific Jeffries tube. Many of them probably connect to another tube, or multiple tubes via a junction, and some must open into hallways and rooms. I'm sure there are at least some that dead-end, but there's probably not a universal answer. Since "Jeffries tubes" is just a fancy way of saying that crawlspace behind the wall you use to fix the plumbing, and they're all over starships.