We review our calorimetric and thermal-analysis studies on the water and the hydroxylamine (HA) aqueous solutions confined within mesoporous silica MCM-41. Confined water revealed a small heat-capacity maximum at around 230 K, at which the temperature under ambient pressure crosses a Widom line. With doping a small amount of HA into the confined water, the maximum became a clear liquid-liquid phase transition (LLPT). We argue to conclude that the HA-doping into water brings chemically a negative-pressurization effect with making a low-temperature phase stable through enhancement of hydrogen-bond-network formation. As the pressure applied to the x_HA = 0.03 aqueous solution increased, the anomalous heat-capacity peak due to the transition became small and moved toward low temperatures. The transition behaviors under high pressure are inconsistent with those predicted previously in LLPT models for bulk pure water. Based on analogy of the behavior of the HA-doped water to pure water, we present a new LLPT scenario for bulk pure water: It predicts that both the first-order LLPT line and its bicritical point exist in a negative pressure region on p-T surface.