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Exhausted what you call a Lightning Network payment channel that has restrictions for one way payments (i.e. from Alice to Bob). When a channel is exhausted, the person controlling that side of the channel has no downside to fraudulently trying to commit to a non-exhausted state. 

For this reason, it is not preferable to have exhausted channels and they are something to be wary of if you are running a full-node. However, most Lightning Network wallets, and OpenNode, will ensure that channels do not become exhausted.