Such as Canada. Which, considering how linked US-Canada trade is, would be instability for the US as well.
Huh, I never thought of Canada as a petrostate.
It'd be fair to say that every country would be affected to some degree.
According to general economics, a collapse of oil demand would lead to a drop in oil price in the near term. In the medium term, only oil that is economically less expensive than the oil price will be drawn out. Oddly enough, with most large and cheap oil already explored and tapped, the most likely continued method of oil exploration will be the horizontal well known as fracking. A frack well, unlike a traditional well, requires constant "drilling" to remain productive. This is why after OPEC tried to glut supply the oil companies in the US cut production and with OPEC reducing production more oil wells are coming back online. A traditional well has a very large start-up cost(drilling) and a low continuing cost (running the pump). A frack well has a lower start-up cost (which may be more because modern wells are designed to be cheaper than traditional oil-rigs), but a higher continuing cost. As a result, they are close to small factories in cost. All this means that oil prices are getting more stable of late, not less.
Now, where does this leave countries? Countries that mostly consume oil as energy will see their energy bills go down (assuming that solar or whatever actually becomes cheaper than oil). Countries that mostly produce fossil fuels will see their profits shrink. Whether a country nets a benefit depends on how much cheaper oil ends up being. If oil ends up being 1/10 the price, then oil countries had better hope they can make a shift to some other economy. If the price of oil ends up being 95% current levels, they will have to diversify, but will not be doomed if they go a little slow.
The other thing is that even if somebody came out with a 100% efficient solar cell that they could make and ship for pennies, it would take years to tool up to produce enough to supplant oil as the fuel of choice. Even if oil gets supplanted, it will take a while before drilling for oil becomes unprofitable.
Finally, just because something has more research budget does not mean that it will experience a breakthrough. We could spend the GDP of California on training people to kill with their brains. Or we could spend a tenth that on designing and building a new generation of close attack aircraft. One of them is going to be a success. The other is going to enrich a bunch of crazy college professors.