The supply will taper out slowly, but the other side is the waste CO2. Because of the climate effect we have to stop using the fossile fuel before we run out.
Why? The damage has already been done, as I mentioned earlier the most optimistic scenarios are not enough to stop the climate change, so why bother? If we want to prevent climate change we need to stop using fossil fuels ~100 years ago which is obviously a challenge. I think we are better off trying to mitigate the effects at this point since we can't stop it.
Damage to the climate has already been done, but the projections are that it can get a lot worse if we don't stop very soon. Most species can tolerate a little higher temperature than they are ideally adapted to, but it gets increasingly more tricky if it gets much hotter. So 1.5 C warmer is way worse then 1 C warmer. There is also a limited speed the species (especially plants) can move to higher ground or more to the poles. So a fast increase is especially bad.
A 2nd point is that CO2 is slowly removed by increased plant growth, but this beneficial effect tends to saturate. So the effecitive half life of CO2 in the atmosphere gets longer if the concentration is higher.
The 3rd problem is that with the permafrost ground there can be positive fedback if much of that melts. It is a bit unclear and we hope it is not yet too late. So the problem may be that while the first 300 ppm of extra CO2 we may end up 2 C warmer, the next 300 ppm may end up 10 C hotter - so the slope from CO2 to temperature can change due to tipping points. This is despite the otherwise more log effect from absorption that makes the direct effect in the atmosphere smaller if there is already quite a bit. The feedback part is not all clear, but there is the danger that this may happen and we should stay on the safe side and not gamble with the worlds future. Even the original 2 K target may be dangerous close to tipping points, and thus ideally going for even lower emissions.
If we would stop CO2 emissions immediately there would still be some climate change, but at a limited level. We are currently at some +1.3 K and from the transfer to the ocean and with no more emissions to effect would even go down relatively fast initially, maybe even below 1 K. So the damage already done is more like the part many species can absorb (though not all). What comes on top is what is the real problem. So it is not yet too late and it is a gradual effect, so less is better and chances are the higher the CO2 level aready is the more negative the effect of future emisions will be.
There is not very much we can do to mitigate the climate effects - building higher dams is tricky with a projected rise in see level of some 5-10 meters in the long run. Using even more AC is only making things worse for the rest of the world. The calulations give higher cost for adopting to the higher temperatures than avoiding them by not burning the coal. Add the costs for adoption to the oil price and we may end up in the $500/barrel range. So ideally we should act (or add corresponding taxes) as if the oil price is that high.