Does "Verb to be" imply something?

"They shocked and angered" is grammatically incorrect in the context used here. It must have some verb (are, were) like your second version.

It does work in this usage "They shocked and angered [somebody], when people..."

By the way, the tense of the verbs should match, either

They are shocked and angered, when the people seek to deprive them.

or

They were shocked and angered, when the people sought to deprive them.

In a comment, John Lawler wrote:

The English verbs shock and anger are causative verbs. They refer to somebody (the subject) causing somebody else to feel shock or anger. The participles shocked and angered can be used as predicate adjectives (with the meaningless auxiliary be, like all predicate adjectives or nouns) to express the state, or as passives to express having the experience; but they can't be used in the active with inchoative meaning.