Chicago Mayor Lori Lightfoot has publicly stated what the city could do to keep the Chicago Bears:

Via Sports Business Journal, a Chicago mayoral committee will recommend that the city consider the feasibility of putting a dome over Soldier Field.
A dome, as reported by Crain’s Chicago Business, could cost between $400 million and $1.5 billion.
Other possibilities include upgrades to the stadium (including significant rebuilding of certain parts of it) and selling naming rights to generate revenue for improvements.
The Bears are most interested in pursuing plans for suburban Arlington Heights.
In the long run, it is not probably not worth it for the city and the others to spend hundreds of millions to keep the Bears. The team would benefit the most from new arrangements. The money spent on eight Bears home games a year will be spent elsewhere in the city. The team is not leaving for another market but just for the suburbs.
At the same time, losing the biggest team in town to a suburb is not a good look for leaders. The Bears have played in the city for a century. They are the most popular sports team in town. Soldier Field hosts other events but it has been the home of the Bears for decades. The loss of the Bears could be added to the narrative of losing companies and residents.
Discounting whether the offer from the city is a viable one – putting a dome on Soldier Field is no easy task – I think this is a necessary political move. The mayor and city leaders need to make a good offer to save face. The big city leader cannot let the big team leave without a fight. And ten years from now, when the Bears are playing in a suburban property that earns the team even more money and the city of Chicago has moved on, there may still be lingering blame for those who let the Bears leave no matter what offer or public statements they made.