Anchor transaction for no expiration channels without segwit

On February 6th, 2017, Nicolas Dorier suggested to the Lightning-dev mailing list that a second timeout was unnecessary in a specific scenario. He explained that TX2 would only be signed by Bob if he received the second output of TX1. Alice must have a fully signed version of TX2 before the timeout expires, otherwise Bob can reclaim TX1/1 once the timeout expires and refuse to sign TX2. However, if Alice has a signed version of TX2, she can broadcast it and immediately close the channel (claiming TX1/0), then claim TX1/1 once the previous transaction is accepted. Dorier noted that Bob need not worry about Alice closing the channel with TX2.