In the wiki's Security Considerations code, the Include a Fail-Safe Mode section says:
While making your system fully decentralised will remove any intermediary, it might be a good idea, especially for new code, to include some kind of fail-safe mechanism:
You can add a function in your smart contract that performs some self-checks like “Has any Ether leaked?”, “Is the sum of the tokens equal to the balance of the contract?” or similar things. Keep in mind that you cannot use too much gas for that, so help through off-chain computations might be needed there.
If the self-check fails, the contract automatically switches into some kind of “failsafe” mode, which, for example, disables most of the features, hands over control to a fixed and trusted third party or just converts the contract into a simple “give me back my money” contract.
What are some exemplar self-checking and fail safe functions that I could look at to see how this is done?