I wrote this in another thread, but I'll repeat it here. If you're not opposed to using mods, the deathofsimreactiontweak mod over at www.deichschafblog.de/s4/sonstige-mods/ works really well. Sims will still get a call but if they are a mere acquaintance, the Sad moodlet only lasts a very short time (like an hour?); slightly longer for friends, etc.
If you don't use mods then there are two ways of dealing with the deaths. Fastest is to purchase the Moodlet Solver potion which costs 500 aspiration reward points. The other option I have found is that calling the Sadness Hotline can alleviate the moodlet by adding another stacking Happy moodlet, but sometimes your sim has to call a couple of times and it won't last for 2 days.