Capstick and Ruark hunting books are replete with stories of guys going into the "long grass" to dispatch a wounded people eater.
They prefer a shotgun over a rifle. They also, as I recall prefer 00 buck, over slugs.
Fact is two barrels of 00 buck is a heck of a lot of lead flying out there, and it penetrats pretty good.
Unless I had to, I'd not go after a wounded brown bear in the bush with any gun, anytime whatsoever. I'd wait for him to die. Or I'd stand back and take a shot at him with a 338 or some such.
If I was walking in there after a wounded lion I'd take a shotgun loaded with 00 buck.
If I was going in after a wounded cape buffalo, well; first I'd make sure my life insurance is paid up. Then I'd probably go in with modern well made, hard cast shotgun slugs fired from a 3 inch magnum.
I've been within a few, like five; feet of wild cape buffalo half a dozen times. They are a very serious and frightening animal. Evey step you take to get closer to them they grow to twice their original size. And they STINK.
When they turn and look at you with those wide dead eyes, your blood runs cold and your heart skips a beat. BTW: when they pick up their nose and point it towards you, and then stop chewing.....well you just might be about to breath your last breath.
I have only been on one South African safari. Our PH, a great guy named "Hine" took me up to and personal with Buffs several times. He was very cautious. He told me that his best friend had been killed by a buff about two weeks prior our safari.
Wild elephants can be larger, they travel in largish herds with animals of all sizes. A big bull or even an Alpha cow is huge. When they see, our scent you they pretty much stop what they are doing (peeling branches from acacia trees) and check you out. They have a habit of turning and facing directly at you. They'll raise their trunks and sometimes trumpet. You can tell they are working on your scent. Then sometimes, they'll flop out their huge ears. Sometimes they'll make a run at you, but in my case they always stopped.
Now when this happened to me (several times) I was armed with a early model .458 Winchester single lens reflex camera!
No one had to tell me to stand stock still.
The thought of wounding one of those brutes and then following him into the brush to finish him off, is just almost unimaginable.
BTW: I was around many elephants for several days, and felt as if I knew them, sorta. The day we arrived on the safari (about 50 clicks from Addo Elephant Park, maybe 200 clicks north of Port Elizabeth) an elephant torn into one of the PH's homes and absolutely destroyed the place. For some strange reason they can go between just standing around and then tearing things up for what appears to be no reason at all. If an elephant wants to tear up a home, or smash a car, there's no way to stop him; short of killing him.
I don't think that now, I'd be able to bring myself to shoot one. There were big ones, middle sized ones, teenagers, aunts and uncles all milling around together, usually in a herd of 20 or so. The calves run about between their aunt's legs. To my mind there is nothing so cute as a baby elephant. I'll kill anything, but I'm not sure I could kill an elephant. They are just too amazing, and too bright.
BTW: You'll see them oftentimes at night. They can walk past you just a few feet away, in dry brush, and hardly make a sound. An elephant can actually sneak up on you, and they sometimes do, just for the heck of it. The ones I saw were totally wild and absolutely unafraid, but they never took us for granted.
I watched an rhino and a massive bull elephant fight over a water hole. It was an amazing thing to see. Guess who usually wins a fight to between an elephant and a rhino?
The rhino.
