I have heard of 1/2 Yom Tov:-i.e. Observing 1&1/2 days YomTov when in Israel, which is as old as antiquity, but 1/2 Shabbos is an entirely new one to me.
Maybe the person is off the East coast of Australia on a ship on Friday nite, and on Saturday morning jumps onto Australia land, so is left with 1/2 of shabbos.
Short of this, I cannot for my life figure out what 1/2 Shabbos implies?