Salvation is by grace, therefore we cannot say Abraham (for example) lost his salvation when he failed to trust God’s promise but accepoted Sarah’s invitation to sleep with her servant Hagar and get a son by her. If salvation is thus bt grace and not at all merited then it is by election. Also since these Old Testament heroes are among the saved (and Jesus talks of Abraham, Isaac, and Jacob being at the feast in the kingdom of heaven (Matt 8:11).
But take another Old Testament hero undoubtedly elected by God, David can he have lost his salvation through the sin with Uriah and Bathsheba? By no means, or we speak of damnation by works!
Yet what then of Manasseh, son of Hezekiah? He also is elected by God as an ancestor of the Messiah, as David was (Matt 1:10), is Manasseh’s salvation lost because of his works (2 Kings 24:3)? If so we are back to salvation by works.