Happiness should be affected for a day or so after some member of the tribe dies. (If they have special bonds, the death of close friends leaves a longer sadness behind)
If there are tribe leaders, Loyalty would be down if the leader is dead / absent, for example.
I believe this system is implemented in regards to food/starvation, as shown in Part 2 of the 50th Devlog Special. It will probably be applied to death too.