This doesn't make sense.
The VPN connection is a tunnel inside your standard Internet connection, which allows you to access a remote network through the Internet. There can't be any VPN without a working Internet connection. For this reason, it's impossible for your Internet connection to need the VPN, because the exact opposite is true: it's the VPN which needs a working Internet connection before it can even be established.
Depending on your operating system (which one, BTW?), your Internet connectivity (dial-up? DSL? Cable? Do you even have a router?) and your VPN software, there might be some way to automatically drop the Internet connection (or disable your computer's NIC) if the VPN goes down; but you should keep in mind that having "a way to access the Internet without a working VPN" is a prerequisite for the VPN itself to come up. Any solution like this will very likely require manual intervention to go back to a working state.