Definetely the valve in the Fill Mechanism (or Refill Mechanism or Fluidmaster) gets faulty. So even the water is full and the floater has pushed the valve rod to the maximum upper level, the water supply is not stopped. If we want to ensure it, after flushing, manually move the floater up simulating full water level. If water supply is still flowing then its confirmed.
The easiest way is to replace the whole Fill mechasism.
Bugi
June 2011