It seems to me that you have cause and effect backwards. I think the most likely chain of events is something like this:

Member gets sick

Member gets rejected from the group (because for each individual in the group, it's better to avoid the sick member - no group selection necessary)

Member dies

So the member doesn't get sick because they're rejected - they get rejected because they are sick. This would have obvious benefits for each individual that rejects the sick member, regardless of the behavior of the rest of the group (https://esajournals.onlinelibrary.wiley.com/doi/abs/10.2307/...)

Could you explain that link between health and status a bit more?

I vaguely remember reading adverse health outcomes in lower status individuals may be linked to the chronic stress attributed to being low status, but can't remember the exact source but this one came up in a quick search:

https://www.sciencedirect.com/science/article/pii/S235228951...