With all due respect to Kip, (and everything he said is correct) I think a simple answer to your question is that we can`t tell a star has exhausted it`s fuel until the light from that event reaches us.

It is the nature of the universe that the fastest this or any information can reach us is the speed of light. So if your looking for a hypothetical example, lets say Sirius goes nova tonight. We
would not know about it until some time in 2008.