Iranian languages
In addition to Old Persian and Avestan, which are the only directly attested Old Iranian languages, all Middle Iranian languages must have had a predecessor "Old Iranian" form of that language, and thus can all be said to have had an (at least hypothetical) "Old" form. Such hypothetical Old Iranian languages include Carduchi (the hypothetical predecessor to Kurdish) and Old Parthian. Additionally, the existence of unattested languages can sometimes be inferred from the impact they had on neighbouring languages. Such transfer is known to have occurred for Old Persian, which has (what is called) a "Median" substrate in some of its vocabulary. Also, foreign references to languages can also provide a hint to the existence of otherwise unattested languages, for example through toponyms/ethnonyms or in the recording of vocabulary, as Herodotus did for what he called "Scythian".
What language is Carduchi thought to have become?
Kurdish
Such hypothetical Old Iranian languages include Carduchi (the hypothetical predecessor to Kurdish) and Old Parthian.
Carduchi