The firstborn of the poor shall feed. The "firstborn of the poor" are the very poor (Jarchi, Rosenmüller). The refer-once is to the poor Israelites, who will "feed" and "lie down in safety" when Philistia is held in subjection.
I will kill thy root with famine, and he shall slay thy remnant. God kills with famine, man with the sword (see 2 Samuel 24:13, 2 Samuel 24:14). When the Philistines had resisted behind their strong walls till hunger had done its work by thinning their ranks, the Assyrian conqueror would storm their strongholds and slaughter "the remnant."