Never say never.
They can hope for a fairly epic collapse for the teams ahead of them, and to eke out a situation where they have one more win than several of them. (Unlikely)
Or, they can work to win 2 more games than the Lions. (Also unlikely) This, sadly, would be the most realistic of those scenarios, so let's take a look at their remaining schedules.
Keep in mind that the Lions own the tiebreaker here, so the Bears truly have to finish with one more win than the Lions to win the division.
The Lions remaining opponents combined are 21-26-1. The Bears remaining opponents are a combined 23-24-1
To get to a better record than the Lions, the Bears simply need to win two more games than the Lions do over these last four. That leaves you the following combinations:
Lions 0-4, Bears 2-2 or better
Lions 1-3, Bears 3-1 or better
Lions 2-2, Bears 4-0
Can you count on any of these to happen, with the Bears defense? Possibly not, but it's the most likely way for the Bears to get to the dance that matters.
But what hurts the most is...
The close loses this season. Five out of the six losses have come by eight points or less. Winning any one of those games, particularly the two losses to the Lions, would have made this season a whole lot more rosy.