I'm new to Blender but have this issue after trying to make a difference with boolean tool with shortcut Ctrl + ⇧ Shift + i cant see the cutter wireframe and can't modify the cutter too.
If you're using the Bool tool, you select the Cylinder, Shift-select the Cube then use ⎈ CtrlNumpad- That should produce this result:
If you use the ⇧ Shift key at the same time the boolean cylinder will disappear because it actually applies the modifier and deletes the cylinder.
In that image I've clicked on the bounding box of the Cylinder to select it, but you could also click the Cylinder in the top-right Outliner panel.
If you now ↹ Tab into Edit mode you'll be able to edit the cylinder as normal and the effect will show in the cube cutout back in Object mode.