I find it strange when someone hears about another's dead lover and he says "I'm sorry for your loss". Why would they apologize when they have nothing to do with his or her death? Is there a better expression, something like "Don't feel sad" or "It's something natural"?
The word sorry doesn't always mean "apologize."
feeling regret, compunction, sympathy, pity,
"Sorry for your loss" means "I feel sympathy for your loss."
My heart feels sore for you. My heart is sore-ry. I am sorry.
sor·ry (sr, sôr)
adj. sor·ri·er, sor·ri·est
1. Feeling or expressing sympathy, pity, or regret: I'm sorry I'm late.
2. Worthless or inferior; paltry: a sorry excuse.
3. Causing sorrow, grief, or misfortune; grievous: a sorry development.
[Middle English sori, from Old English srig, sad, from sr, sore.]