While I've one or two students come down to the wire in the past few years, I've honestly never had this problem before. Typically my seniors all reach a point of equilibrium in the final weeks where they're happy to do the work just to have something to do. Even in my Core Senior classes in the past, students still showed up, read the novel, completed the final assignments when May rolled around. Maybe it was nostalgia that kept them going, or not wanting to screw up anything before graduation. For (a few of) my Juniors, however, there's no such built-in good will. These students have checked out and perhaps don't plan on mentally returning until next August.
So what's there to do? There's the old "threaten them with not passing" but that only works if they can't get above a single digit percentage in the fourth quarter. Completing just one of the next five assignments will accomplish that. Twitter will say "make the learning more engaging and meaningful for the student, then they can't help but be hooked!" That sounds great on paper...but sometimes you need/want to teach them things they wouldn't be "hooked" on on their own. I'm confident with some prodding, some of the students will improve, though there's a few that will likely parachute into the sunset. I just hope they're ready to go when they return next year; graduation is still over 200 school days away.