Yes, Churchill has a bear jail. During polar bear season, there is a regular bear patrol. If a bear is reported as being too close to town, an attempt is made to scare the bear off by, essentially, firing a 'firecracker' in its direction. If that doesn't work, the bear is tranquilized and taken to the Polar Bear Holding Facility.
We didn't get to see inside the facility but were told that the inside is kept dark, the bears are kept in cages close to each other (not something they normally like) and are only given water to drink ... essentially, making the place somewhere they don't want to return to.
The bears are tagged and then flown far away from town and released. If the bear returns it gets a second chance. A third time, though, and they are out.
We were fortunate to see a bear lift on our last morning there.