Cheron, it is possible for the peeps to go to the sandbox after a death. My 61 year old was not weak and went directly there after her husband died. My little Becky was also holding her stomach in the pic I posted. I started a new generation a few minutes later, and she hadn't become sick by then, not to say she may not have but I don't think that is exclusive to being sick.
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All you need is trust, and a little bit of pixie dust.