I was ponder this the other day actually. You could have third parties who acted as a sort of escrow and signed when some result was achieved. You could distil the ‘some result’ into code even, so these third parties could validate and run the code. There could be competition for trustworthy and fast third parties, which would build their reputation.
These signing third parties could be anonymous or known. Their merit could rest on evidence of prior signings. They could even just be applications running somewhere.
I thought the benefit of this over it living on the network could be security and sanity checking.
For security, the keys could remain unknown by the network - either physically or just in an unknown location on network.
For sanity, a human element may be useful. If a bug in the code is being exploited, draining an account, an element of validation could allow an interpretation of the contract, rather than pure, cold, hard, code. Perhaps some signers would even have legal backgrounds in contract law?
Although running contracts within the network may have strengths, there are also weaknesses. I often wondered whether there was a use case for smart contracts whe ethereum was being launched. It is obvious there is, but is there another way that is a sort of hybrid like this, between traditional and smart contracts?