Drew hadn't expected to hear Mila say she would remember him. He had reached a point where he was able to be conscious even when Leo was asleep. He wasn't in control of his body so he couldn't see her but his ears were still working.
She said everyone deserved to have someone remember them when they were gone. That sounded oddly personal. Did it have anything to do with her mother?
He didn't know much about her situation but knew her mother died and her stepmother mistreated her according to the cat. If she felt her mother had been forgotten, it would also explain why she cared about being remembered more than being successful in a traditional sense.
That sort of logic didn't make sense to him because he had always been ambitious. If someone was good at something, they should strive to be the best. Simple as that. But he had never lost anyone the way she had.