It is generally agreed that no-insulation (NI) high-temperature superconducting (HTS) magnets do not quench because of the turn-to-turn energy-releasing bypass unique to NI. However, these magnets, especially with high operating current and low ambient thermal capacity, still occur unexpected quenches when the current through the magnets suddenly drops to zero (i.e., the sudden-discharging quench). Here, we report this kind of quench, which is different from that widely-reported quench happening during charging (i.e., the energizing quench). Here, a demonstrative coil with 655-turns, 350 A operating current, and 4 K conduction cooling, is used to prove this sudden-discharging quench, and a simulation model is built to reveal the quench dynamics. Results show the turn-to-turn heat triggers the initial partial quench in the inner coil turns and then the induced overcurrent spreads out the quench like an avalanche to the outer coil turns.