"To finish the fight" means to complete or end a conflict or battle, usually with a strong determination and perseverance. It conveys a sense of determination to overcome obstacles or opposition and achieve victory or resolution. Full definition
The veteran's experience showed as he was able to overcome a slow start and end up finishing the fight with elbows and knees with only 35 seconds left in the fight. (slickstermagazine.com)
They are still more than capable of finishing a fight if another dog starts one. (pawster.com)
They will often take on much bigger dogs and will always finish the fight if someone starts one. (lovethatpet.com)