I summoned an invisible marker armor stand, and gave it a scoreboard score in an objective called "pid4", and set it to 1. This is in multiplayer, by the way. I set the sidebar display to the "pid4" objective, and it showed that the armor stand's score was still set to 1.
After that, I relogged from the server, and when I logged back on, the sidebar was empty, and the armor stand's "pid4" score was not set at all. The armor stand still existed, but had no scores. I tried this with setting multiple scores at the same time, and I still got the same results.