Unlucky Sims can only die of old age and perhaps drowning. If they die by any other method, the Grim Reaper will point and laugh at their misfortune, and then resurrect them.
If an Unlucky Sim has 4+ hours of sleep they will wake up with the "Feeling Unlucky" moodlet.
Whilst under the influence of the "Feeling Unlucky" moodlet, Sims are more likely to lose games, burn food and cause fires.
If University Life is installed and they rant against death via a megaphone, they'll likely die without receiving any sort of warning. But the Grim Reaper will still humorously resurrect them afterwards. This can be considered the fastest and easiest way to encounter the Grim Reaper without any repercussions (other than losing all the moodlets the dead Sim once had).