BJT cut-off mode

Cut-off mode is the BJT region where both junctions are reverse-biased. Neither junction is forward-biased, so there’s no carrier injection anywhere and no current through any terminal. The transistor is off.

For an npn, cut-off means the base-emitter voltage sits below the turn-on threshold: $V_{BE}$ less than roughly 0.5 V, so the EBJ isn’t forward-biased. With no EBJ forward bias the emitter injects no electrons into the base, so $i_C\approx 0$, $i_B\approx 0$, $i_E\approx 0$. Only the tiny reverse leakage currents of the two junctions flow, negligible for hand analysis.

Cut-off is the open-switch state in digital logic, the complement of saturation (the closed-switch state). A BJT used as a logic switch swings between cut-off (output high, transistor an open circuit) and saturation (output low, transistor a near-short with only $V_{CE(\text{sat})}$ across it). It never lingers in active mode, since active mode dissipates power and is reserved for amplifiers.