Miners can burn their money, but it is way to expensive to run such hardware to do so. As previously discussed, Bitcoin is infinitely divisible. I could see us breaking down Bitcoin 8 more decimal places when we have calculated that only about 10,000 BTC are left in existence. However this "trashing coins" process is one of the cons of having a decentralized currency. No central authority issues wallets, so there is no verification such wallets exist. Clients should check if the address coins are being sent to is in fact a valid address, but other than that there is almost nothing we can do about it.