Recent observations of fast radio bursts (FRBs) indicate a perplexing, inconsistent picture. We propose a unified scenario to interpret diverse FRBs observed. A regular pulsar, otherwise unnoticeable at a cosmological distance, may produce a bright FRB if its magnetosphere is suddenly "combed" by a nearby, strong plasma stream toward the anti-stream direction. If the Earth is to the night side of the stream, the combed magnetic sheath would sweep across the direction of Earth and make a detectable FRB. The stream could be an AGN flare, a GRB or supernova blastwave, a tidal disruption event, or even a stellar flare. Since it is the energy flux received by the pulsar rather than the luminosity of the stream origin that defines the properties of the FRB, this model predicts a variety of counterparts of FRBs, including a possible connection between FRB 150418 and an AGN flare, a possible connection between FRB 131104 and a weak GRB, a steady radio nebula associated with the repeating FRB 121102, and probably no bright counterparts for some FRBs.