It depends on the system. Single-tank electric softeners typically regenerate at a set time overnight when water demand is lowest — usually 2 to 3am. During the regeneration cycle, hard water may pass through to the supply. For most households, water use at 2am is negligible and this is not a practical problem.
Twin-cylinder non-electric systems (Harvey, Kinetico) have one cylinder softening while the other regenerates. Soft water is available at all times, with no periods of hard water breakthrough. This is one of the main practical advantages of the twin-cylinder design.