I don't believe there's ever been an eraser tool as part of Word's drawing
tools. As JoAnn says, you can select drawn lines and shapes and click
Delete. But you can't erase portions of them.
What you may be recalling is the Eraser tool on the Tables and Borders
toolbar, which can erase borders or the boundary between cells (to merge
them). In Word 2007, when your insertion point is in a table, the contextual
Table Tools are displayed. The Design tab of the Table Tools has a group
called Draw Borders thathas the Eraser button on it.