I'm working through an Assimil book, and I found this sentence:
Ich hoffe, er bleibt nicht lang.
Shouldn't it be
"Ich hoffe, bleibt er nicht lang."
I thought that, in a sub-clause, the verb and the subject were reversed.
Your first example ("Ich hoffe, er bleibt nicht lang") is correct. But it may be even better to say:
As it stands, you connect two sentences, but this does not change the word order in the individual sentences. There is simply no rule that says it should.
might with some bending and effort be understood as the semantically strange statement
(though this is (more) usual with the subclause before the main clause - so a less but still quite strange statement would be "Bleibt er nicht lang, [dann] hoffe ich") while
is the same as the more complete
Also note that in three of these four examples, the subject is still (correctly) before the verb! The verb switches with the subject in questions, while you probably think of verb and object ("Er bleibt nicht lang." -> "er nicht lang bleibt" in subclause and "Bleibt er nicht lang?" in a question).
There are two different kinds of subclauses relative to the main clause: coordinated subclauses and subordinated subclauses.
Coordinated subclauses keep the usual word order:
Subordinated subclauses have another word order:
The changed word order in subordinated subclauses might yield a reversion the order of subject and verb, but this can also be achieved in coordinated subclauses as the subject need not be in first position in German.
So the correct word order depends on the ordination form of the subclause.
So the first sentence is correct. Your alternative has wrong word order.