No mine really ever “runs out”. There’s always going to be some of whatever is being mined left. The point at which a mine is abandoned is when the concentration of what you’re mining in the rock you excavate is too low to justify operating the mine. It stops being economically viable.
If you have the desire, resources, and complete lack of self preservation (abandoned mines are lethally dangerous, DO NOT ENTER THEM) you could still dig up some trace amount of gold/coal/salt/whatever from a mine.
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