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
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.