Which pipe from the big tank are you talking about? Post a pic showing tanks and pipework!Pipe from big tank (I'm not a plumber!) is putting water into header tank. Not at a great rate mind, but it is occurring.
The two tanks will usually share a common cold water feed, which tees off to the ball valve on each tank. Apart from that there should not be any pipes linking the tank.
If the coil has gone the water level in the big tank can rise; but this will cause water to flow out of the overflow of the big tank, not the small tank.