Empology
Saying "I'm sorry" for something that isn't your fault, as a way to show empathy. This word is a portmanteau of "empathy" and "apology."
"So my dog died last week..."
"Oh wow, I'm really sorry!"
"It's not your fault!"
"I know, that was an empology."
"Oh wow, I'm really sorry!"
"It's not your fault!"
"I know, that was an empology."