Coins only exist at addresses. A transaction takes coins from one address, and sends them to another. If you think these coins still exist, what address do you think they're at?
These were taken from various addresses, and sent nowhere. They aren't in the addresses they came from -- you can check that, the blockchain doesn't lie. They weren't sent to any new address. It's impossible for a new transaction to send them somewhere new, because they don't exist at any address anywhere in the blockchain.
Couldn't you alter the code to scrape the fees from the blockchain when it parses through all of the transactions?
You can't scrape them from the blockchain, because they aren't in the blockchain. For paycoin and peercoin and others that destroy fees this way, the fees are verifiably and irrevocably gone. You can't put coins into a transaction if the coins don't exist.
With a hard fork (i.e., new code, and the new fork of the blockchain supersedes the old one) you can do lots of things. With a hard fork on bitcoin you could increase the maximum number of coins to a billion and send ten percent of every transaction to your own wallet. You just need to get 51% of the hashing power to agree with you, and then convince the world to use your fork of bitcoin rather than the original.
But you still can't put coins that don't exist into a transaction. You could create any number of new coins you want (in new blocks), but that has nothing to do with the destroyed fees.
Just saw your update:
If you burn the fees, then why even collect them? It is ultimately a tax on the coin owner since they are not used to incentivize miners.
Peercoin burns the fees (among others) and their FAQs explain the reasoning. It doesn't make much sense to me either.