Is there solution for event where nobody would mine some coin?
No, there is no solution for such a scenario because it is a non-existent problem. Bitcoin is designed to eventually stop issuing new coins altogether. Miners will then be incentivized by transaction fees alone. It is a built-in feature.
...And if there were no miners validating new blocks, then Bitcoin would cease to exist because transactions couldnt be confirmed. The whole network relies on miners to secure the blockchain and prevent double-spending. If we remove that, then Bitcoin no longer has a purpose.