We study the late-time (t\gt 0.5 days) X-ray afterglows of nearby (z\lt 0.5) long gamma-ray bursts (GRBs) with Swift and identify a population of explosions with slowly decaying, super-soft (photon index {{{G }}x}\gt 3) X-ray emission that is inconsistent with forward shock synchrotron radiation associated with the afterglow. These explosions also show larger-than-average intrinsic absorption (N{{H}x,i}\gt 6× {{10}21} c{{m}-2}) and prompt ?-ray emission with extremely long duration ({{T}90}\gt 1000 s). The chance association of these three rare properties (i.e., large N{{H}x,i}, super-soft {{{G }}x}, and extreme duration) in the same class of explosions is statistically unlikely. We associate these properties with the turbulent mass-loss history of the progenitor star that enriched and shaped the circumburst medium. We identify a natural connection between N{{H}x,i}, {{{G }}x}, and {{T}90} in these sources by suggesting that the late-time super-soft X-rays originate from radiation reprocessed by material lost to the environment by the stellar progenitor before exploding (either in the form of a dust echo or as reprocessed radiation from a long-lived GRB remnant), and that the interaction of the explosion's shock/jet with the complex medium is the source of the extremely long prompt emission. However, current observations do not allow us to exclude the possibility that super-soft X-ray emitters originate from peculiar stellar progenitors with large radii that only form in very dusty environments.
