If by fail safe you mean that powering off the reactor makes it cool down then the Navy uses fail safe reactors. Water is used as the moderator to absorb radiation. When water is heated its density decreases (edit), thereby making it a less good moderator of radiation. This effect lowers reactor reactivity and heat output. This effect is combined with various devices to produce what is called an inherently safe design. Losing power will not make the reactor have a fuel element failure or melt down.