In your example, all verbs are in the past and Bill was still ill at the moment that John said so:
John said that Bill was ill.
However, at the moment that you are saying this, Bill may not be ill anymore, that is unsure. In case you want to express Bill's illness both at the moment John said so AND at the moment that you reported this, the following construction is needed:
John said that Bill is ill.
In this sentence, Bill is still ill at present.
To express that Bill's illness was over both before you or John spoke, you can say:
John said that Bill had been ill.
In this sentence, Bill is not ill at the moment of speaking, nor was he ill at the moment John spoke. He had been ill before John talked about it.