As what they have said, to play Finishing move, you need a legal target upon playing the effect which is a stunned character.

Upon resolution, you need a stunned character because it specifically targets a stunned character, so if you CoTA in response to Finishing Move, your character is not KOed because it no longer have the stunned characteristic upon resolution of Finishing Move.

In TA/Rogue case, getting stunned is a condition for their triggered ability to trigger. Upon resolution of their triggered effect, it does not need to check if the character is still stunned.