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There is a absolute limit on the cost of coal: What it costs to get it out of the ground and into the powerplant. Even if the price of coal per unit weight goes down to 0 it will still have a cost to transport it. I think that in the medium term that is what coal is up against; a solar alternative that is cheaper in the long run.

The less important coal becomes on a global scale, the less infrastructure and expertise that will be maintained for extraction and processing. This type of lack of supply should drive up prices as well. Consider the ease of buying and maintaining a horse vs a car.

Investment will descrease which will decrease supply making what is still dug up more expensive.

It probably will become cheaper, since as volume goes down mines that are only marginally profitable now will close, leaving only the most efficient.