Context: I’m reading a children’s book that does not use kanji so it’s a bit difficult to figure out meanings sometimes.
This passage talks about forest bears hibernating and gives us the sentence:
はるまで ねむっているはずです
I understand this all to mean that they will sleep until spring comes. But I’m not understanding the use of ず here. Any thoughts?
This is はず, which is a grammar point:
They’re expected to be sleeping until spring.
It’s not ず – it’s はずです。
It means “is expected to”
春まで眠っているはずです means that the person who is the topic – is expected to sleep until Spring.
P. S. Ninja’d by @soggyboy さん 
Although if you did find a verb ending in ず, that would mean “without [verb]ing.” It’s formed by attaching ず to the negative stem of a verb (ねむる⇒ねむらない⇒ねむらず) and is often followed by the particle に.
(Addendum: Technically though it’s actually not the -ない stem but the -ぬ stem, which is older/more formal. With the vast majority of verbs, the two stems are identical, but する is one notable exception: する⇒せぬ⇒せず)
It’s はず。はず is used when you expect something to happen.
Haru made nete iru hazu des.