An offchain signature is a promise that you may include some data in a future update. What if the last person in an offchain transaction withholds their signature? You must be ready either way and let it timeout. How does the Lightning Network deal with signature withholding?
OK, I re-read things again. If you withhold one step, the other party can always exit using the time box at the latest state they fully know. This is achieved by the two-phase exchange: first, keys for new state slowly, then secrets for fast invalidation of old state.
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So, if the other party has little money left, or is in no hurry to get it, they can always keep you hanging for a week, and you should choose them so it doesn't happen, especially in multi-hop cases. (Also, you must be online often, and commit updates to remote backup.)
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Simpler explanation: first you add a new valid state, then you invalidate the old one. There is a point where both states are valid, and one or both parties considers the transaction incomplete.
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