I agree with A_Camera above. I'm not an electrician but if a live wire came loose and touched the outer case it would become live at mains voltage. If the case is connected to earth (PE) then current would flow down the earth line instead of returning via the neutral line and there would be an imbalance between live and neutral which is detected by the breaker, and it should trip. I believe this is set to trip at around 30mA (?), someone might correct me here.

In terms of star earth points then I've always used a fairly large piece of metal as the star point, and then each device is individually connected to it. I'm not sure why I use a large block but I read somewhere years ago that the backplane of a control cabinet should be a certain thickness if used as the PE star point. Perhaps it ensures low resistance so the 30mA is reached? It might also help make sure each device is at the same earth potential, avoiding current flowing along the earth wire but someone might correct me on that one.

The other reason (I think) for connecting the case of an enclosure to earth is for RF shielding, but this is more likely to comply with industrial installations, although still worth having this benefit at home.

I always check continuity using a multimeter between the earth pin of the plug (when not plugged in) and a random series of points around metal cases etc. There is probably a value of resistance it should be below but I've always made sure the value is very low and close to zero.

Those are my thoughts on it anyway. Maybe post some pictures here as first look, but if you are not sure ask a qualified person to check it over.