Panelizing multiple PCBs onto a single panel is a cost effective way of prototyping. V-groves are usually used to separate the different PCBs, making it easy to snap them off. The picture above depicts what happens when the V-grove hits a copper pour such as a ground plane.
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