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When running a lightning node on a mobile phone, unannounced channels are a good fit as I may stay offline and don't want to do any routing.
But how do I know whether my channel partner might close the channel due to
  1. Me staying offline for too long
  2. Me not transferring any sats
I totally get that an inactive channel is a wasted ressource for any node operator and there is an incentive to close it eventually. But does any node publish the details on when exactly it will close a channel?
Someone correct me if I'm wrong ...
Because your node is offline, for them to close the channel they'd perform a forced close which doesn't require your participation. The details of this close are published on-chain.
If you are concerned about fraudulent forced closes (they publish a channel state that gives them more of the channel balance than they deserve), you'll want to setup a watchtower.
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I'm not really concerned about fraudulent forced closes, I'm more searching for a node who says "it's ok if you don't open your wallet for a month, but for compensation we require a little more fees than others" or something like that.