Comment 1 for bug 811787

As explained in the 0.47 release notes (the version the eraser was added in Inkscape), the eraser only applies to the selected objects and ignores the unselected ones see http://wiki.inkscape.org/wiki/index.php/Release_notes/0.47#Eraser_Tool).
Marking this report as duplicate of Bug #230476 "eraser tool needs option to ignore selection" (it already requests a different behavior that looks like the one you are expecting).