He again protested about the work on the event of the planning being rejected by authority.
I think "on the event of the planning" is intended as a description of "work", and its meaning isn't quite clear, so let's look at the sentence without it:
the skeleton of the sentence is
He protested about the work being rejected.
The meaning is that he protested, and what he protested about was that the work was rejected.
That is a gerund clause, or "gerund-participial clause". It functions as the complement, or object, of the preposition "about". The subject of the clause is "work", the gerund is "being rejected" (which is a passive form).
Some other examples of that use of "being":
He liked being accepted. (direct object of "liked")
Being helpful was important to him. (subject of "was")
Going back to the deleted bit, "on the event of the planning", it would make more sense as "on the planning of the event". I suspect there's a mistake in the original.