Omissions of "that" in a relative clause [duplicate]

I am not clear on when the word "that" can be omitted in a relative clause. I only know that when the modified noun is the object in the clause, the antecedent "that" can be omitted. Are there any other such situations? How about the following sentence:

Students should be skeptical about everything they are told.

I am not sure whether everything is the object, and if not, whether this sentence is correct.

What are the students told? - everything (well probably not absolutely everything!) - so everything is the object, and the sentence is fine.

Let's have the long version: Students should be skeptical about everything that they are told. The fact that there's a pronoun (they) in subject form between the relative pronoun (that) and the verb, tells us that they is the subject. That's one easy way of deciding. What is probably throwing you is that the relative clause is in the passive, so it looks a bit strange. But just look for that pronoun.