Unfortunately, this is not necessarily true.
As an illustration, change "coin" into "coal"
A lot of miners may mine coal and extract it. You may have far too many miners and the coal seam is not very rich.
However, if there are no power stations to use it to generate electricity and no fires burning in people's homes to keep them warm, the coal piles up and is not consumed. As a commodity, it is only as valuable as it's usefulness. Mining more coal will not encourage people to burn it. There is no incentive to pay the miners if the coal is not actually used.
The supply outstrips the demand. The price of coal falls, mines close, communities destroyed.
This is what happened to the coal industry in the UK during the 1980's
I'm not attacking Libertycoin, I'm pointing out the flaw in your economic modelling.
well to make it a fair comparison:
the coal is no longer mineable, there is however a fixed amount of coal around in the world, divided over many different people.
Now there is service that still mines, but different commodities however (e.g. gas/oil etc). These commodities have a value and are sold. This service now goes to all poeple who have still some coals and offers a fair price to take it over. This coal is now handed over to the miners of the new service.
Over time, the coal will get more rare. and it will become more difficult to buy this from the owners who have some coal left (they might think there property becomes more valuable if they wait longer)
You can still ask the question, what should i do with all this coal as miner, but the economic models is correct. No supply, and a actual demand, will drive price higher!