Blender Version
Broken: 2.8x

Short description of error

I believe this is a remnant from the old outliner, but if the new outliner is supposed to sync selection between itself and 3D view, it looks like a bug.
When adding or deleting bones in armature edit mode, outliner keeps its selection highlighting, irrespective of what's actually selected in 3D view.

Exact steps for others to reproduce the error

1. Load the .blend
2. Note the two selected bones, they're also highlighted (selected) in the outliner
3. Delete these two bones
4. Note that no bones are selected in 3D view
5. Note that two other bones became highlighted (selected) in the outliner, even though they're obviously not selected.

From here, ctrl (or shift) clicking another bone in the outliner will update 3D view selection according to what's highlighted in the outliner.

Adding a bone will also not affect outliner selection.