The open magnetic flux of the Sun, the component of the solar magnetic field that forms the heliospheric magnetic field, is known to be concentrated into coronal holes, regions of low plasma density where the solar wind escapes easily. There also is evidence for concentrations of open flux in the vicinity of active regions. In this paper we explore the possibility that there is an additional component of open flux. We argue that open magnetic flux will reconnect with closed magnetic loops and that this process will distribute a small fraction of the open flux into a uniform, radial component in regions that do not underlie the overexpansion of the magnetic field from coronal holes. This additional component of open flux will facilitate the escape of energetic particles from solar flares and also the escape of plasma to form the slow solar wind.