The structural nature of high-density amorphous ice (HDA), which forms through low-temperature pressure-induced amorphization of the "ordinary" ice I, is heavily debated. Clarifying this question is important for understanding not only the complex condensed states of H2O but also in the wider context of pressure-induced amorphization processes, which are encountered across the entire materials spectrum. We first show that ammonium fluoride (NH4F), which has a similar hydrogen-bonded network to ice I, also undergoes a pressure collapse upon compression at 77 K. However, the product material is not amorphous but NH4F II, a high-pressure phase isostructural with ice IV. This collapse can be rationalized in terms of a highly effective mechanism. In the case of ice I, the orientational disorder of the water molecules leads to a deviation from this mechanism, and we therefore classify HDA as a "derailed" state along the ice I to ice IV pathway.