An optical fiber sensor system and method for monitoring a condition of a linear structure such as a pipeline is provided which is capable of providing continuous monitoring in the event of a break in the sensing optical fiber or fibers. The system includes at least one sensing fiber provided along the length of the linear structure, and first and second interrogation and laser pumping sub-systems disposed at opposite ends of the sensing fiber, each of which includes a reflectometer. The reflectometer of the first interrogation and laser pumping sub-system is connected to one end of the sensing fiber. The reflectometer of the second interrogation and laser pumping sub-system is coupled to either (i) an end of a second sensing fiber provided along the length of the linear structure which is opposite from the one end of the first sensing fiber, or (ii) the opposite end of the first sensing fiber. Before any break of the sensing fiber or fibers occurs, each reflectometer redundantly monitors the condition of the linear structure over its entire length. After any such break occurs, each reflectometer will continue to receive signals up to the point of the break from opposite ends of the structure.