Allowing the battery to completely discharge is bad for it.
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# Why did my computer turn off/hibernate when the battery got to 10%?

When the charge level of the battery gets too low, your computer will automatically hibernate (that is, it will save all of your open documents and applications, and then turn off). It does this to make sure that the battery doesn't completely discharge, since this is bad for the battery. If the battery just ran out, the computer wouldn't have time to shut down properly either.

You can change what happens when the battery level gets too low by clicking your name at the top of the screen, selecting System Settings, and then opening the Power settings. Look at the When power is critically low setting. You can choose for the computer to hibernate or shut down. If you choose shut down, your applications and documents will not be saved before the computer turns off.

Some computers have problems hibernating, and may not be able to recover the applications and documents you had open when you turn on the computer again. In this case, it is possible that you could lose some of your work if you didn't save it before the computer hibernated. You may be able to fix problems with hibernation though.