Ok this is my theory of what would happen after she dies;
He'd just straight up become cold, he wouldn't let anyone come close, and would snap at anyone and everything. In other words he would become pretty insane, probably would stare a massive painting of her, constantly asking himself why he didn't ask her to change at her last moments. I also have the feeling that she would regret not turning into a vampire right before she's about to die, due to the fact that she knows whats going to happen to him, and it would be too late to change anything so she dies.
An other theory would be that she changed into a vampire at her last moments. She would turn to him and ask, or he would beg on his knees and explain the amount of pain and suffering he'd go through, how he wouldn't want to change into that "monster". Knowing well that he would go insane after seeing how he's reacting, she'd agree and become a vampire. Obviously that would mean that they would be together for the rest of eternity but at least, neither of them would have regret.
. _. so y e a h, its either one of these theories, for our "epilogue"
I wish she turned into a vampire. I don't know I feel sad imagining the girl will die while he will live forever. Imagine the grief.