Refer to an example: the author uses a variety of strategies to make the characters live in the reader's mind. Here, survival and breathing are verbs.
Live can be understood as "lively" in translation, but it is not an adjective in grammar.
There is a suspicion of ambiguity at the end of the sentence in his play. If there is no context, there can be two understandings here. A similar ambiguous sentence in English is actually very common: put the box on the kitchen table. This sentence also has two interpretations.
So your original sentence can be advanced in the drama to avoid ambiguity: in the drama, shakes let his characters live through their language.
=================================
Everything said downstairs is wrong. It is impossible to modify characters at the end of a sentence. As an attributive modifier language, as an adverbial modifier verb makes. If you must modify a character as an attribute, you can modify it as follows:
Schacks brought his characters in the play to life through their language.