The same question could be asked about the bitcoin network once all 21 million bitcoins are mined. The strength of the network is obviously backed by the processing power of the individual "authenticator" participants. I'm assuming we have a solution to that. Don't we? Isn't that the point of transaction fees? If we don't, my proposal might be what we're looking for.
I'm merely bootstrapping from a different starting point. All of the coins are pre-mined. The decentralized distributed exchanges extract a fee to put digicoin tokens (exactly like bitcoin) into circulation (vaulting/storing the fiat USD) and pay it to the "miners" or "authenticators" who use their bitcoin clients to verify the transaction for you. There would be no currency exchange exposure at this point.
The transaction fee is proportional to the amount of fiat dollars they would spend to pay for their rigs, their electrical costs, and other attendant capital costs. It's a known cost at the outset, not exposed to the BTC/USD exchange rate as it is now, thus less risk to the miners. Mind you, electrical costs are still denominated in fiat currencies. This wouldn't be an issue if you could purchase electricity and hardware in BTC contract prices (interchangably). I fully intend for the "miners" to be incentivized.
Processing power is still used to secure the network as it is now in the bitcoin network. I'm merely presenting a 1:1 BCT-to-fiat conversion until the all of the pre-mined coins are exchanged for fiat (which sits in a vault executing the occasional bailment service).
I'm starting out with a transaction-fee based system first, as opposed to the mining incentive system then fee. It's almost like bitcoin, but from a different starting point.