This is plasterboard or something with a void about an inch back

This is the wall plug

The hole here is actually so big that the wall plug would fall through into the void if I put it back

I can’t move the radiator up or down or left or right because it is fixed and even if I knew how to disconnect it I wouldn’t want to spill black water everywhere and ruin the carpet, so I am thinking I should use the same holes but get a bigger plug

What about the plastic ones for plasterboard that sort of butterfly out when you fix them in?