I don't own 'demon slayer', but I do own Lu. Mentions of suicide and depression.
Muzan learned two things after that night.
First, this human was a mess. Lu was a mess to the point it would be annoying if she did anything other than work and lay in her bed. Some days she didn't even work.
Second, Lu took better care of him than she did herself. That annoyed him a bit. Even if she was having one of her bad days (read; curling around herself in bed and sobbing), she would still get up when her alarm went off to feed him. Or when he paced by the doors to go out.
It was rather confusing for Muzan. This human was more willing to look after a literal cat (even if that cat was him), more than she was willing to care for herself.
At first, he didn't care. He had no reason to since she continued to feed him that (reluctantly delicious) cat food and let him roam about. His only priority was returning to his previous form.
However, after that night, Muzan added another item on his priority list. Keep Lu alive. He would rather have her be his patron then another random human who might be more annoying so he couldn't let anything happen to her... yet.
So he began acting... civil. On days when she wouldn't (read; couldn't) get out of bed, he would make himself at home on her covers. He wasn't sure how to comfort people, but her sobbing became less annoying when he laid with her. On days she drowned herself in work, muttering to herself. He would keep an eye on her, just to ensure she didn't do anything rash. He even bothered scolding (read; meowing insistently) when she didn't eat that day.
It wasn't until two weeks later that something shifted.
It was another bad day. A day where Muzan begrudgingly resigned himself to staying with the human who simply laid in bed. Lu was just staring at the ceiling. A blank look behind her eyes that reminded Muzan of a corpse. It was almost nostalgic for him really. Usually Lu wouldn't speak during these times, which was fine for Muzan since he hated small talk. It seemed today wouldn't be a silent day though.
"... I'm sick, y'know." Lu murmured softly. So quiet Muzan wasn't sure he actually heard her at all. "Not like a cold or something, but something in my head is just... wrong." She didn't seem to be talking to him. More like muttering to herself. Lu closed her eyes again, likely trying to sleep. She did a lot of that.
Sick. Being unable to leave a bed. Some wrong.
That hit a bit to close to home for him.