They won't lose any money to fees, because they won't broadcast their transactions-to-self, they'll just include them in blocks that they create.
So, evil miner does:
Gets some myselfcoins.
Creates transactions that pays themselves the myselfcoins, and pays BIG fees.
Does NOT broadcast those transactions.
... eventually mines a block that contains those transactions (they're a miner, they can put whatever transactions they like in their blocks).
Then does that again and again, re-using the same coins, getting richer and richer from the FEES+10%