In the light novels, in this scene, it was very apparent that he was talking about Celty when he said “a monster at my deathbed”.
“You were lucky I happened to be nearby’… It’d be a little hard to say that.”
“Your injuries were bad enough that you had to be rushed to the hospital, so I was fifty-fifty about helping you.” Kine spoke, blandly, of his own opinion.
“Honestly speaking, rather than that knife in your stomach, it’s the bruises that seem worse. It looks like your insides are in a bad state; you did well fighting Shizuo like that.”
With this, Izaya looked towards the side of his abdomen. Indeed, there was a projectile-type knife imbedded in it. But Shadow((courtesy of Celty)) coiled around the wound, suppressing the bleeding as much as was possible.
“You shouldn’t remove it. If you let it bleed your fifty percent chance would drop to ten.”