Scanned proton pencil beams carry a low-dose envelope that extends several centimeters from the individual beam's central axis. Thus, the total delivered dose depends on the size of the target volume and the corresponding number and intensity of beams necessary to cover the target volume uniformly. This dependence must be considered in dose calculation algorithms used by treatment planning systems. In this work, we investigated the sources of particles contributing to the low-dose envelope using the Monte Carlo technique. We used a validated model of our institution's scanning beam line to determine the contributions to the low-dose envelope from secondary particles created in a water phantom and particles scattered in beam line components. Our results suggested that, for high-energy beams, secondary particles produced by nuclear interactions in the water phantom are the major contributors to the low-dose envelope. For low-energy beams, the low-dose envelope is dominated by particles undergoing multiple Coulomb scattering in the beam line components and water phantom. Clearly, in the latter situation, the low-dose envelope depends directly on beam line design features. Finally, we investigated the dosimetric consequences of the low-dose envelope. Our results showed that if not modeled properly the low-dose envelope may cause clinically relevant dose disturbance in the target volume. This work suggested that this low-dose envelope is beam line specific for low-energy beams, should be thoroughly experimentally characterized and validated during commissioning of the treatment planning system, and therefore is of great concern for accurate delivery of proton scanning beam doses.