There are umbrellas that fold into really tiny space, small enough for a large pocket, for example. Just put it into a plastic bag when going into a store to avoid leaving a trail of water drops. No need to leave your umbrella behind for some scumbag to steal it. I bet even in Japan the cops wouldn't be amused if you went to report the theft of a single umbrella you purposefully left behind unguarded, so what are you going to do?