This may seem like bait, but I’m asking a genuine question. This happened to my girlfriend where she rejected her former best friend (in a nice way, even saying they could still be friends) and later got insulted, told to kill herself if she was so depressed, and said she never wanted to see her again. Some people say this girl is mean, crazy even, and others say she had the right to say that because she was hurt and my girlfriend should have said yes even though her best friend was a lot less mature and younger than her. They were more like siblings than anything.
Definitely not okay. And it depends on your definition of “normal”. Is it common? Somewhat. Going as far as to say “kill yourself” usually isn’t part of it but insulting someone after being rejected isn’t rare. It depends a bit on the age.