Miners would be paid through transaction fees alone.
Paid what?
Paid DestroyCoins from the sender.
How do you secure the DestroyCoin network?
I can see where this is headed, but I also like watching train crashes in movies so I'm enjoying playing this out.
The DestroyCoin network will be secured in the same way the Bitcoin network will be after all Bitcoins are mined. Computing power will compete for the fees gained when a block is found.