No, the ferrule is on the end with the tool, as noted, to prevent splitting. The cap on the other end is just there to hide the tool marks from the turning center, so they can make it cheaper.
I never buy ferrules for shop-turned tool handles. I make them in minutes from short pieces of copper tubing or copper collars. An alternative is to buy octagonal brass compression nuts and turn them round on the lathe using a parting tool. (They turn rather easily.) The nuts are available in a wide range of sizes and have the advantage that they can be threaded onto the end of wood handle for a positive grip. The photo shows a few examples from my shop. The ferrule on the parting tool in the foreground was made from a brass nut.
I have seen a carriage bolt used on wood handled chisels, cut the carriage bolt so it seats through the handle butted up againt the tang of the chisel-so if you strike the chisel with a hammer the force is seated against the metal part of the chisel-
Have seen strike buttons of brass or dense wood on some hand chisels. should work as a decorative element or to protect the handle it forcefully setting a tapered tang.
Could not find the right words to bring anything up. What I would suggest is getting some brass rod on the diameter you want and just turn your own. easy to do with HSS turning tools.
I suppose those were first used on turning tools that had a tapered shank on the chisel, set into the handle. With some vibration and wood seasonal movement, the turner would need to bang that end of the handle on a hard surface to reset the chisel. The end button would prevent any splintering or damage to the handle. You could use a short connector bolt or nut, but they would have an internal hex hole on the end. A cheap solution is an electrical box blank knockout seal.
If there's no tool jammed into the butt end of the handle, there isn't any splitting force for the bling to counteract. We're not talking about double-ended dental pics, for example, that have tools on both ends.
When I first started turning handles I would drill the hole first and then I had a drive center that fit in this hole. I would bring the tailcenter up and turn the whole handle. When I removed the tailcenter there was a hole so I just drove a brass tack that I had handy into that hole to cover it up.
Now I do things in reverse. I have custom made hole sizes for my live tail center and I put the predrilled hole of the handle on that. Then I turn the rest of the handle but the butt end will end about 1/2" or so from the drive center. Then I cut this off and carve it away and there isn't a hole.
On a chisel a solid end-cap for striking is sometimes called a bolster, but more often a butt plate, as it is on the butt of a rifle.
I suppose the term bolster shares its origin with the bolster on a muzzle loading rifle - there is a part of the lock called the bolster which serves a similar purpose at the back of the lock (it is the restraining piece which effectively forms the back end of the barrel, sometimes screwed in place, more often an integral part of the lock casting.
Also, when a ferrule is put on the butt end of a tool it is often called a hoop, even though it is exactly the same thing as the ferrule on the tool end.