What's the grammatical item for "Some in tears" in this sentence?

Solution 1:

The sentence "Family members waited by the mounds of debris - some in tears" exemplifies a phenomenon called gapping.

Definition: "Gapping" can be defined as a sentence with the main verb deleted but its dependents - subject, objects, adjuncts etc. - left in place. The deleted verb can be recovered from the previous sentence. The sentence will typically, but not necessarily, be introduced by a conjunction, like and, or. Linguists most commonly indicate the deleted verb with a strike-through line, so that "Mary likes beer and Sally wine" would be indicated like this:

(1) Mary likes beer, and Sally likes wine.

Gapping generally requires a great deal of parallelism between the previous clause and the gapped clause, in terms of word order, grammatical functions involved, and semantics.

Application to example: The example in the question has a gapped clause "some in tears". It's missing verb can be understood from the previous sentence, i.e. it's waited. "Some" functions as the subject of this deleted verb. "In tears" is an adjunct of the verb (additional, optional information). The structure is shown below:

(2) [_subject Family members] waited [_adjunct by the mounds of debris].
[_subject Some ] waited [_adjunct in tears].

The previous clause and the gapped clause are quite parallel, as is typically the case, in that both feature a subject and an adjunct as the only elements of the verbal head and place them in the same position.

Solution 2:

They searched for the missing throughout the night under generator-powered flood lights as family members waited by the mounds of debris - some in tears.

Syntactically it's a supplement, the verbless analogue of the non-finite clause some being in tears (an absolute construction).