I can't see a case for bringing the engine to idle rather than shutting it down completely. If a bearing is running out, a 25,000 rpm idle might be just as damaging as 50,000 plus rpm. By leaving the engine at idle, when it is providing no torque and just burning fuel to self-sustain, you are achieving nothing.
Your sick donkey might subsequently seize before you need it for landing. Had you shut it down for transit and subsequently restarted it, it is more likely to be usable for when you really need it.
In the event, my own preference would ideally be to transit single engine, restart the engine for landing if required, but not rely on it and carry out an OEI profile just to be doubly safe. Having the second engine running for landing will prevent unnecessarily busting a limit on the good engine, which would be a great shame if the chip turned out to be a very minor thing.
Unless, of course, the Flight Manual or your company policy says otherwise. The time to change the checklist IS before you have to do it for real, which I think is why Gabra1 is asking.
