Thanks - I must confess I didn't really think about the different shades of meaning that the Mary sentence could have. Very interesting!

Yeah, but phrasal verbs are tricky and mean - in a different context "to live on" if followed by, let's say, "the rent generated by the seven houses he owned" or "the residuals of the hit television series she wrote" or "the fat of the land", gets an entirely different meaning... That's sometimes a bit confusing.