Brace yourselves, this is going to happen. I honestly think this makes too much sense.
The Jags save almost 4 mil if they trade him. If they keep him, they pay him 22Mil to backup and 15Mil next year after even after they cut him. The team taking on Foles takes on 15Mil, but it would be NON guaranteed, meaning a negotiation would certainly be in order. His 2020 money is very similar to what Ryan Tannehill had before he renegotiated and bet on himself after being traded to the Titans.
The Jags also have a bunch of picks in the first 4 rounds. I think they'd be willing to give up one to get rid of Foles.
Foles has been with Nagy (KC), Lazor (PHI) and Flip (PHI and JAX). Think he'd jump at a chance to play in Chicago. The Bears get a QB familiar with their system (which seems to be big for Nagy, being that Daniel and Bray have hung around for a couple years), and can sell the fanbase on the fact they're getting a SB winning QB.