Assuming that kṣāraka is derived from kṣar "to flow", then the Proto-Indo-European root is *dʰgʷʰer- "to flow, move forcefully, with derivatives referring to ruin and destruction" (from the AHD, also see IEW 487-488). The Avestan derivatives also have the "flow" sense. I guess dust flows, and is associated with ruin.
One Greek derivative of *dʰgʷʰer- is φθείρω phtheirō "to scatter, destroy", which is probably the source of φθείρ phtheir "louse". As the OED says:
Ancient authors derive ancient Greek φθείρ louse < φθείρειν to destroy (see PHTHARTIC adj.), as they believed that lice were generated spontaneously in decaying flesh. Modern scholars generally accept this derivation.
φθείρ was borrowed into English thru Latin in the form phthiriasis, a lice infestation (of the eyelids apparently).
I really hope today's extreme etymology is true, because it's awesome.