Bombardier Inc. took the extraordinary step Thursday of agreeing to give up almost half its stake in the struggling CSeries jet program to the Quebec government in exchange for a $1 billion lifeline.

The government deal confirmed fears that Bombardier’s balance sheet is more stretched than previously disclosed, as its ambitious bid to compete with rivals Airbus Group and Boeing Co. with the CSeries weighs on the company. It recorded more than $4 billion in write-downs in its latest quarter, mostly reflecting the declining...