Is there solution for event where nobody would mine some coin?
The blockchain doesn't need miners to stay alive. The blockchain is essentially just data or records stored on a hard drive, paper, or even written on a wall. What miners do is extend the length of the blockchain and make changes to the data. So, in a scenario where nobody mines Bitcoin for a year, it simply means the data will stay the same; you can't change it, but nobody would lose their coins or keys. You can still propagate your transactions; they just won't be written into the blockchain. The moment someone turns on a miner and finds a block, the transactions will start going through.
There is also another important function that miners perform: they keep the difficulty high enough to ensure the security of Bitcoin. However, it's important to note that even today, miners aren't actually building the blockchain 24/7 despite trying to do so. It’s only when a block is found, which happens on average once every 10 minutes and takes less than a second to occur.