I couldn't care less about whose spirit is fading away....

When you get that message it is the game giving you a chance to keep the sim that has died in the game instead of culling it. Now if there is a sim you want to keep, go to the tombstone or urn of the deceased sim and click on it. You'll get an option to strengthen the connection or something like that, and that ghost won't be culled. Any sim can do this.