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?
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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