It's a blockchain, there's nothing to stop the old chain from continuing. While miners continue to mine, it'll exist.
And what kind of application will the tokens have after block 315000?
If you're referring to the ERC20 WYV tokens - they'll be used to pay fees on the
Wyvern Exchange, and vote on protocol upgrades through the
Wyvern DAO!
If you're referring to the Wyvern coins on the old blockchain - I don't know of any application, I'm not going to develop that chain any further (but anyone who wants to certainly can).