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... die apud imas Esquilias finis incendio factus, prorutis per...

finis incendio: Lewis & Short, s.v. "finis," IIB, gives examples of the gen. and dat. following "finis" with the meaning "end": “in hoc (aequo judicio) uno denique falsae infamiae finis aliquis atque exitus reperiatur,” Cic. Clu. 3, 7: “dicendi finem facere,” id. Sest. 65, 136; cf.: “si placet, in hunc diem hactenus ... finem disputandi facere,” id. Rep. 2, 44 fin.: “scribendi,” id. de Or. 2, 55, 224: “maledictis,” Ter. Heaut. prol. 34: “injuriis,” Caes. B. G. 1, 33, 1: “vitae finem afferre alicui,” Cic. Phil. 6, 1, 2; cf.: “quando finem habet motus, vivendi finem habeat necesse est,” id. Rep. 6, 25: “finem judiciariae controversiae constituere,” Cic. Verr. 2, 1, 2, § 5. Allen and Greenough, New Latin Grammar, Sec. 366 b , describe the dative syntax with nouns: b. The dative is sometimes used without a copulative verb in a sense approaching that of the genitive (cf. §§ 367 . d , 377):— lēgātus frātrī (Mur. 32), a lieutenant to his brother (i.e. a man assigned to his brother). sceleribus (Tac. Ann. 6.36), agents of crime. [Cf. sēditiōnis ministrī (agents of sedition.] miseriīs suīs remedium mortem exspectāre (Sall. Cat. 40), to look for death as a cure for their miseries. [Cf. sōlus meārum miseriārumst remedium (Ter. Ad. 294).]