Legally and historically, the right to exploit resources has belonged to those who have legal or political control over the territory they occupy. When it comes to fossil fuel resources, in a world increasingly altered by climate change, it seems to me that the moral circumstances for such right holders have changed. While they could once have claimed that there was no evidence of their extractive activities providing harm on a global scale to present and future generations, climate science has now clearly shown that all incremental fossil fuel burning will increase the level of climate change the world will experience, with all the harm, dislocation, and death likely to accompany that.
The old dictum about your right to swing your fist ending where my nose begins seems appropriate here. The legal obligation of states to consider the global environmental commons is recognized in international law. In an advisory opinion on nuclear weapons, the International Court of Justice held that:
The environment is not an abstraction but represents the living space, the quality of life and the very health of human beings, including generations unborn. The existence of the general obligation of states to ensure that activities within their jurisdiction and control respect the environment of other states or of areas beyond national control is now part of the corpus of international law relating to the environment.
In an ideal world, perhaps resource holders would accept that their past profits were an unjustified windfall, defensible only because of our prior ignorance about climate change. Pragmatically, however, most people feel as though having undertaken an activity in the past entitles them to keep doing it. Obviously, this is unacceptable if humanity is going to deal with the problem of climate change.
The pragmatic solution seems to be providing some compensation for those who will lose out on hypothetical wealth, due to the need to keep fossil fuels underground. Such compensation, however, should be recognized as a pragmatic mechanism for achieving carbon neutality more quickly, not as a recognition that the resource holders had a pre-existing right to extract every burnable molecule at hand, regardless of the consequences for others. As such, it seems legitimate to restrict such compensation to being used in ways that advance the necessary global transition to carbon neutrality. For instance, by funding re-training programs or the establishment of low-carbon enterprises. That holds the possibility of achieving necessary emissions reductions, while at least blunting opposition in regions dependent on fossil fuel resources.
All that said, we cannot expect the prospect of reasonable compensation to secure support for climate change mitigation in the regions most economically dependent on fossil fuels. It is hard to imagine oilfield workers in Fort McMurray or Riyadh happily abandoning their right to extract fossil fuels, just because there is a program to train them to make solar panels instead.