Once again, a few caveats, before we start:
- "Passive" applies to clauses, not sentences. Only simple sentences, without subordinate clauses, can be called "passive sentences", if the main and only clause is passive.
- Therefore, there is no "active mood" for a sentence to be in, and no "passive mood" that you can transform it into. That's not the way it works.
In a clause, application of the passive transformation requires
a transitive verb with a subject and a direct object. The direct object is promoted to subject, and the original subject is out of a job. The main verb changes to a past participle and is preceded by some form of the auxiliary be; which form depends on whether it is preceded by some other auxiliary verb controlling its form.
In the sentence in the question
- People believe [he may be fired].
the noun complement clause (that) he may be fired, the direct object of believe, is already passive. It's the passive of somebody may fire him. Note that it's followed the rule: past participle, form of be, subject thrown away, old object becomes subject.
The main clause
is transitive and may be passivized, producing
- That he may be fired is believed by people.
Note that both clauses are passive. The that complementizer is usually optional, but it's required here because the that-clause begins the sentence (as the new subject).
However, no he will appear in the main clause, certainly not as subject;
he occurs in the subordinate complement clause, and passive only operates inside its own clause. So there's no way passive can move a noun up one clause; there are rules that do that, but not passive.