Probably a cheat, but a piezo disc setup would give you zero power audio capture and with others to power basic processing, you would be able to do something, though may find yourself shouting during testing, though a capture cone to focus the audio onto the piezo would help immensely. Though I'd seriously have to sit down and work out what surface area of pezios and vibration levels and as such power you could produce. Though could mitigate that with some larger capacitors to capture all the passive sound and low level power the piezo's will capture/produce during the day. Triggering processor to check for your keyword and instigate an action.
Not analogue, but certainly would be Zero power.