When you design PCBs for work, cost-effectiveness is a big factor. To help you out in the that department, you usually design your board to be a big panel. This panel is then CNC routed to contain a V-groove. This is as the name implies, a V-shaped groove that runs between the individual boards on your panel. When you have pasted, stuffed and reflowed your boards you simply snap them off. This brings in the cost-effectiveness, to be able to process many tens of boards at once.
Anyway, back to the topic. You usually want to have a copper pour on your boards, be it ground or a power plane. Sometimes it just so happens that you send your Gerbers to the PCB fab but they reply back saying the V-groove will cut the copper, is this OK? Well, in one of my prototype boards I just told them “go ahead”. This is what came back:
The result (click for bigger)
It looks nasty, but the board is totally usable. You wouldn’t sell this to the customer, and actually I had one short caused by the bent copper near a connector. If you know the risk and you’re in a hurry, you can certainly let the V-grooving cut the copper. But I would advise to fix it anyway.
With typical V-groove specifications, you need to leave a guard area of 0.4 millimeters around the border of the board.