Whenever my sister and I play Minecraft, I am the host of our LAN world. Usually, when I was to leave whatever world we were playing on, she was usually booted from the world, being that it had been closed; however, lately, whenever I, as the host, have logged off, I have noticed that she is still in the world for a few more minutes (she can't do anything, because the terrain disappears, but she is still there for a few moments before it kicks her out).