Blocks that destroy bitcoins are valid. In such a case, the fee would be gone forever.
Onkel Paul
+1
That's happened before.
+1
As has been stated. If a miner chooses not to claim the full reward that they are due, then the unclaimed portion of the reward simply ceases to exist. This has happened before.
If the claimed portion of the reward is greater than or equal to the block subsidy, then you might think of it as "destroying" bitcoins that used to exist (some or all of the transaction fees). They are removed from circulation forever (assuming no significant change to the bitcoin protocol).
If the claimed portion of the reward is less than the block subsidy, then you might think of is as "failing to mint" some coins in the first place. They simply never come into existence and are never put into circulation. This reduces the total bitcoins that will ever be created (assuming no significant change to the bitcoin protocol).
How you choose to think of it is really a matter of semantics. Technically the system doesn't differentiate between the portion of the reward that is "subsidy" and the portion that is "fees".