What would happen if all Bitcoin is mined and all Bitcoin is lost?
I guess that at that point bitcoin would not exist anymore, that's it. You are mentioning bitcoin but it's the same with anything else: what happens if we extract all the oil available on our planet? It's done, no more oil. What happens if we kill all the elephants? No more elephants. And so on. Anyway a scenario like the one you are mentioning is extremely unluckily to happen, why would people choose to deliberately get rid of something that has a high value?
It's possible that all BTC can be mined but I don't think all will be lost like we send it to an unknown address that doesn't exist and BTC can't be recovered anymore. Why would someone do that? For what purpose? Keep in mind that the reason why we buy BTC and HODL is to earn a big profit, but that act we said earlier is just an opposite of it.
BTC is only just a currency. It's not the same as anything. And it's not like an ordinary currency, but it is decentralized and has a limited supply. BTC can keep on circulating but I don't think it's possible for an oil to do that once it was already used. Luckily there are lots of sources of it, so it won't ran out easily.