My doctor told me to pull a wound together and apply the glue over the skin surface of the wound, not in it. I'm sure some glue gets into the wound that way, but would be eliminated as Bill described.
I wish I'd know about using water to release the bond. Several years ago I was gluing something at my workbench. The spout on my cyanoacrylate glue bottle was clogged, so I squeezed the bottle harder. Nothing happened, so I squeezed even harder. Blockage released suddenly and I flooded my hand and the workpiece with glue, effectively gluing myself to my workbench. Fortunately, my debonder was within reach and I was able to free myself, but not before suffering some minor blistering from the heat released form the curing glue. It's amazing the variety of accidents one can have in the workshop.