RE: .22 caliber
Eventually a shot to the chest or gut will kill but it is hardly humane.
I have a mate who shoots scrub bulls weighing around 800-1000kg with a 22/250rem but I wouldn’t recommend the practice. With a 22 cal shot placement has to be spot on for a clean kill and you have to be very careful about what projectiles you use as most are very fragile and have little to no penetration, and the only reliable shot is a head shot and due to the explosive nature of most .224 pills that can damage a good trophy.
But saying that I have culled some big Red Deer with a 223rem but all shots were placed in the throat and destroying the major arteries and death was very quick but most did run some distance.