(How) Does the human digestive system process petroleum jelly, aka petrolatum?
There are controversial case reports about systemic absorption of paraffin used for constipation. These reports mention systemic effects of paraffin absorption and one of them report liquid paraffin accumulations in
abdominal visceral organs. (full text article about paraffin) 


  Liquid paraffin is indigestible and is absorbed only to a limited
  extent following ingestion.


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  As inert substances the ingested mineral oils mostly are excreted
  intact in feces and to some degree in urine. However, some absorption
  form the small intestine has been observed (Stryker 1941). Using
  radiolabeled mineral oil, it was established that the amount absorbed
  in rat was appr. 1.5 % (Ebert  et al. 1966).


  (full text article)