In circuits, dependent sources (or controlled sources) rely on some control variable (i.e., a voltage or current in the rest of the circuit). If the control variable is 0, then dependent voltage sources become short circuits and current sources open.
Often the control variables represent some signal for audio or video. The constants represent some amplifier gain.
In ECE212 — Circuit Analysis, if a circuit consists only of controlled sources (and resistors) with no independent sources, then we assume the circuit will have only zero voltages and currents. The precise mathematics are in Prof. Najm’s lecture notes.