We have a slave configured as "Take this slave on-line when in demand and off-line when idle" with an Idle delay of 10 minutes. When the idle period expires, the slave status page shows the following error:

Connection was broken

java.io.IOException: Unexpected termination of the channel
at hudson.remoting.Channel$ReaderThread.run(Channel.java:862)
Caused by: java.io.EOFException
at java.io.ObjectInputStream$BlockDataInputStream.peekByte(ObjectInputStream.java:2554)
at java.io.ObjectInputStream.readObject0(ObjectInputStream.java:1297)
at java.io.ObjectInputStream.readObject(ObjectInputStream.java:351)
at hudson.remoting.Channel$ReaderThread.run(Channel.java:856)

Since the slave was intentionally taken off-line, it should not be in an error state.