1. Many musicians have families and work to create an inheritance for them. If there is no copyright past death there is no inheritance.
So, when I die, can I still have the company I work for continue to pay my family for the work I did when I was alive?
Copyright laws that extend beyond the death of the artist are an abomination.
No, but the money that you were already paid does go to your family. Your company will also pay your family for your unused vacation time (at least this is true when you leave or are fired, so I assume it's true if you die unexpectedly). The term is "deferred compensation", and that's what royalties are.
Copyright terms that automatically expire at the death of the artist are what would be completely unfair. In addition to the danger of a young artist dying unexpectedly, as another poster described above, it would provide reduced incentive for older artists to continue producing works. A fair copyright term would be a fixed length, completely regardless of what happens to the creator. Otherwise, the monetary value of the work is directly dependent on the age, health, and, to some extent, luck of the creator.