As far as I understand a photon is produced, or "born", whenever an electron moves from a high energy state back to its normal energy state.
It would be reasonable to think that the exact opposite happens, and that is indeed the case (with some optional extra details that aren't important).
Photosynthesis is one of nature's applications where this effect is directly used (in a very complicated process that scrapes off tiny amounts of energy in a long chain of electron transmissions, and that finally does an oxyhydrogen gas reaction without blowing nearby things to smithereens, which is darn cool) to build up high-energetic chemical stuff from low-energetic components. Though, regardless, electrons get excited anyway, whether someone makes "good use" of that or not. And then, some time later, something happens (we cannot tell what). One thing that may happen is a different photon being emitted, another thing is some unknown, random chemical reaction that needs energy taking place. Often, that whatever unknown reaction is a source of radicals. This is one of the reasons why we get skin cancer from UV light, by the way.
what happens when light stops [...]
If you stand in a huge and pitch-black cavern, and shine a torch, the light will only carry so far.
That is not what really happens. Three things occur here. First of all, photons get scattered in space, and space tends to "consume" stuff very eagerly. The mathematical formulation of that is "distance attenuation". While one might think that being away twice as far halves the amount of photons, in reality it cuts them down to one quarter ("inverse squares"). Evidently, something that works this way very quickly smothers anything that is "very finite" such as e.g. light coming from a torch. It doesn't matter quite so much for "practically infinite" things like the sun, but in principle, the same is of course true. So, the amount of light shed by a torch in a large cave isn't terribly huge.
The second thing is that "somewhat close to zero" and "zero" are the exact same thing. Your eyes are unable to see single photons (well your eyes are technically able to receive a single photon, but neither does the biochemical pathway, nor the processing work that way). There is plenty of light remaining in that pitch black cave (well, plenty is maybe somewhat of an exaggeration), only you are not able to see it.
Lastly, there is air in your pitch black cavern, and there is dust and vapor in the air. All of these will absorb and/or reflect photons to some extent. The "reflect" part is why you can often "see" the light orb when in fact actually that's not possible at all (what exactly is it that one would expect to see!). On the other hand, light that is reflected away isn't going to hit your eye (other than incidentially, after having been reflected at least one more time). What's absorbed is gone, one way or the other, so it doesn't illuminate the rest of the pitch black cavern.
the colour black "absorbs light" - does this mean the colour black is "eating" photons?
The opposite is the case. All materials absorb light to some extent. Some only absorb very little of it, and only in a very narrow frequency range. Some absorb huge amounts, and in a large frequency range. Those materials appear black to you because black is your conception of no light meeting your eye. It's not the black absorbing photons, but you see black because they've been absorbed. Note by the way that something can very well appear black and emit lots of photons at the same time (you are only able to see a relatively small range).
Things can be quite deceptive. Glass appears to absorb no light at all (look out your window!) but that isn't true at all. It only absorbs a relatively small (~8-10%) amount of the light that you can see. If you consider e.g. UV light or infrared, things look completely different!
does the same "photon death" happen when a photon hits the retina in a persons eye
Yes. The photon excites an electron in a rhodospin molecule (there are a few variants of these) and it's "gone" after that. The transferred energy causes a structural change in the protein which activates a G-Protein. That one kicks off a certain amount of the second messenger cGMP. When there's enough of that around (not the case for a single photon), the cell decides to fire, and then a neural network on the back of the retina which clusters some areas together in some obscure way gets to decide whether or not to forward an impulse to your brain. Only then, after another few thousand iterations, you have a chance of actually seeing something.