I always think of it as the full saying: "speech is silver but silence is golden". So not saying anything is worth more than saying something. "Actions speak louder than words", I suppose?
Plus it's a sagacious-sounding way of telling someone to SHUT UP. :P
I'd also take it as advice not to put too much value on words: "It is better to be thought a fool, than open your mouth and remove all doubt." and "if you argue with a fool, no-one could tell the difference." ;)
As for silence killing people... I understand what you mean, but I think that's a different context.