That's why you have a multi-channel redundant FBW control system.
An unstable aircraft means you don't have to have as large control surfaces. Every pound you save in structure means less other structure to support it, less fuel to push it etc. Works out that every pound you cut saves around 5 pounds in total.
The end result is that you can build a much smaller aircraft for the same range/payload. Overall, for a combat aircraft, the sums come out in favour of making them unstable.
There is no evidence that anything occured on this occasion which involved the FBW system or that it was a factor in the decision to eject.