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I have zero idea what this construction is called. Here are a few examples that I've just whipped up:
He was fired, and his friend punished.
He was robbed, and his brother kidnapped.
The idea is that the second part of the sentence takes the same verb as the first. Kind of like continuity of the sentence.
Those are gapping constructions. Gapping deletes a repeated verb and other repeated constituents, leaving behind two constituents, one of which (in Ross's formulation) must be inside the verb phrase and the other must be outside the verb phrase. A classic of grammatical analysis was Ross's paper Gapping and the order of constituents, which showed that the basic word order of a language predicts whether gapping will go from left to right (as in English), or from right to left.
Here is the Wikipedia account: Gapping. (I see that BillJ also gave the correct answer in a comment.)
It's an example of coordination (i.e., two elements linked with "and"). Elements common to the two coordinands can often be omitted in the second one.
Eg, coordinated subjects, common predicate:
John and Mary went to the shops.
Coordinated verbs, common object:
John noticed, and bought, a painting.
Coordinated objects, common subject and verb:
John bought a painting and a tapestry.
Coordinated predicates, common subject:
John bought a painting and examined a carving.
Coordinated predicates with direct vs indirect objects, common object:
John greeted, and chatted to, Mary.
Coordinated predicates with the same verb, but different complements or adjuncts:
John walked slowly and Mary quickly.
Mary waited patiently and John on tenterhooks.
He was fired, and his friend punished. (your example).
