The way I see it is there are three types of “inbox exs”.
The lonely inbox ex. He probably wants to hookup or even get back together. He realizes he lost something great and now regrets his life. He also can’t get any other girl to smile at him so he’s feeling small and lonely. It’s sad.
The angry inbox ex. He’s victimized himself, made you a “b*txh*, and told all his pickup truck friends that HE broke up with YOU. In his message, he makes use of all the curse words he’s learned in his however many years on earth and let all his “feminazi” frustration out on you. It’s also sad.
The apologetic inbox ex. He’s moved on, realized though you may have damaged his pride, he may also have hurt you. He has a new girlfriend but his conscience is keeping him up at night. He’s in your inbox to make amends. This one is no longer sad.