As far as I know, all supernovae that have been observed in the past century, after peaking in its luminosity, gradually went dimmer. Thus the view that a supernova explosion indicates the death of a star is quite justified. For example, sn1987a, which in 1987 was brightest object in the LMC, is now hardly visible even with the most powerful telescopes.
However, the object which illuminates the crab nebula is a very powerful source, inspite of being 1000 years old. It is commonly believed that this object was first seen by Chinese astronomers 1000 years ago. My contention is that the Chinese witnessed a star birth, and not a star death.
According to biblical chronology, stars were created on the 4th day, 6000 years ago. If the literal interpretation of the bible is correct, a star birth event observed 1000 years ago would imply that the star is 5000 light years away.
Let me quote from
http://hcs.harvard.edu/~jus/0302/bester.pdf
"To summarize, our best estimate of the distance to the Crab Nebula is 5,600 light years, although we can say with certainty only that it lies between 4,000 and 7,000 light years."