Unfortunately, it will do the latter.
What it will mean is that you can only sell if somebody else buys. We think of it like a customer boycott: If I don't buy products, they're going to stay on the shelves. However, that is not true in capital markets. You can only sell if there's a buyer.
In fact, it may well mean that the buyer is somebody who cares less about climate change than you do, because they're willing to buy those stocks, so you actually no longer have a seat at the table to engage. Not only do you lose the higher returns from carbon, but unfortunately—and I wish this were not the case—evidence is that emitting firms earn higher returns, perhaps because this is an externality, not an internality. You not only lose those higher returns, but you also lose your ability to engage with these companies.