In regard to the dead family member, I'm assuming you have an urn/headstone and haven't invited the ghost back into the family. If you do as Dellena suggests, you will no longer have a ghost of this family member, and all relationships outside of your household will be lost. You can't keep anything in your inventory as it emptied when you save the household to the library. If you do this and want to save things, you have to put everything out in the house before saving it, and then put those items back into inventory after the move.
In regard to your bug, if I am understanding what you are saying at the end, the problem happened in a new save game with a new sim. If this is the case, you've already confirmed that it isn't just the first save. If I've misunderstood, then the first thing I would do would be to make a new game and test it out with a new sim. If it happens in more than one save, then it's not related to one save, household, or lot (so saving to the library and moving would not help).
Do you use mods? If so, have you tried removing them and playing to see if the problem is still there? I would also repair the game through Origin and delete the cache files to see if that helps. I've played quite a few police officer sims and not had this problem, and hopefully we can all help you figure out why you do.
