While very little of the writings of Carthaginians has survived, the language itself (Phoenician/Punic) is well understood because a very close relative, which was mutually intelligible with it, has, however, survived: Hebrew. So if anything did turn up, we'd be able to read it.

Contrast this with another ancient language: Etruscan. Although we have a number of longish texts in the language, we can't translate much of them. Etruscan has left no descendants, and Emperor Claudius's books on the language haven't survived. There is one bilingual text of more than a few words (the Pyrgi tablets). The other language is Phoenician. We can read that.