It's a broken flask with that thing in it so the seller could maybe get rid of both of them at once. Separately they were both intended for something but don't go together. I can't tell you much else from that picture.
It´s hard to know what it was used for. It likes an antique torpedo bottle.
I doub it is an apothecary or medicine.
The finish is broken and the topper has nothing to do with this bottle.
I bet it had a cork.
Sorry, what's 4 inches long, the bottle or the stopper thing? At first glance it looks like a torpedo bottle but the proportions are a bit weird for one, they usually were more or less tapered equally on the top and bottom. And if the bottle is four inches long it's certainly not a torpedo bottle. There is a possibility that this is a very badly damaged drug store window display bottle that someone found in a dump. The shape fits in more with those than with torpedo bottles. Drug store window display bottles were fanciful bottles that were used to decorate the display windows of drug stores in the past. The bottles always looked ridiculous and impractical because they were meant to inspire the public's imagination, not to actually be used. They often had round bases and metal stands like torpedo bottles, and always glass stoppers.
The body of the bottle was about 4" long. Definitely smaller than the average torpedo, and the neck I think would be too narrow for a torpedo. the top is chipped but didn't' appear broken. It looked like it might have been ground and polished.
The stopper/dropper was about the same length as the bottle. It was long and tapered and extended to about the bottom of the bottle.
That is incredibly strange then and I haven't got the faintest idea what it is. It looks very real but from your description sounds like something that shouldn't exist. Maybe it's from somewhere really far away, like the Middle East or something. Some country where they used very different bottles than we did. Looks nothing like any foreign bottle I've ever seen either though.