Luke 24:23

In Ancient Greek, the accusative case is used as the logical subject of the infinitive in what's known as the accusative and infinitive construction (accusativus cum infinitivo). Thus, in this phrase αὐτὸν ζῆν, the pronoun αὐτόν serves as the subject of the infinitive ζῆν ("to live"), yielding the meaning “for him to live” or “that he may live.”

"In general the subject of the infinitive, if expressed at all, stands in the accusative."

(cf. Smyth §1972)

See Herbert Weir Smyth, A Greek Grammar for Colleges (New York: American Book Company, 1920), §1986, available at Perseus Digital Library. Additional overview available in the Wikipedia entry on Ancient Greek infinitives.