Flexible sensors capable of detecting large strain are very useful for health monitoring and sport applications. Here a strain sensor is prepared by applying a thin layer of conducting polymer, polypyrrole (PPy), onto the fiber surface of an elastic fibrous membrane, electrospun polydimethylsiloxane (PDMS). The sensor shows a normal monotonic resistance response to strain in the range of 0-50%, but the response becomes "on-off switching" mode when the strain is between 100 and 200%. Both response modes are reversible and can work repeatedly for many cycles. This unique sensing behavior is attributed to overstretching of the polypyrrole coating, unique fibrous structure, and elasticity of PDMS fibers. It may be useful for monitoring the states where motions are only allowed in a particular range such as joint rehabilitation.