Recently I got skype update on my android phone. I started it and found that sign in after I have signed out becomes simple. Just click on the "recent" user.
It even does not ask a password, what is reasonable on so personal device as phone (but I guess this is configurable).
But, this was not the story. Now the story.
Day later I send a message via skype and signed out. Usual thing, right? The unusual thing was: several hours later I found a notification about incoming skype message (with text).
The same time my wife said me that I was "online" in her skype contact list.
So, once more and slow: after I have signed out from skype (and after I have closed the app) I still received incoming messages and was marked as "online".