Ableton Live has 3 different options to monitor a track; Auto, In, and Off. “Auto” will allow you to hear the audio input (post fx) of a track only if the track is record armed. “In” will always allow you to hear the audio input (post fx) of a track regardless of whether the track is record armed or not. “Off” will mute the audio input from that track. Also note that when monitoring is set to “In”, you will not be able to hear the playback of a recorded clip until you switch monitoring back to Auto.
This monitoring behavior is also the same for midi track input for played notes.