I haven't read the rest of the responses but her is my take.
While this story is interesting and it is seemingly amazing that this cat has some special sense that folks are about to expire... I think we may getting the
"Cat Before The Hearse!"
Perhaps the really sick GIVE UP when the cat curls up beside them because they have heard the rumor that Oscar predicts death... could it be that death is a response to a the cat rather than the cat responding to impending death?