How do narcissists deal with a partner's illness?

I would have to say that the competition for attention, the all-consuming jealousy, the societal expectation for them to act somehow compassionate or loving when they are incapable of this and their general distaste for any demonstration of human frailty or imperfections (which sickness represents for them) would send them packing quickly, if not physically, certainly emotionally. I think I would prefer for the narcissist to take a hike than hang around and rage for attention while I was trying to recover. Count your blessings.

My narcissist left me five days after I had broken my ankle, and I was in a wheelchair ... after 11 years together. They have no empathy, none. My advice is to run and don't look back. (If you can run on a broken ankle.)
 
The spouse's illness is an effrontery to the narcissist's delusions of omnipotence, invulnerability, and perfection. She is rendered imperfect, a drag on his resources, a weakling. Narcissists hate the weak, the old, the young, the sick, the emotional - because they remind them of their own suppressed emotions.
The narcissist - always above commonality and the law - resents society's expectations of him. He does not understand why he has to waste his precious time on damaged goods. The sick spouse becomes a source of negative narcissistic supply, a silent condemnation of the narcissist, a pointed (and sore) finger, an embarrassment, and a stark reminder of the grandiosity gap - the abyss between reality and the narcissist's fantasies.
 
The N I was unfortunate to be with severed all contact with me after I was admitted to hospital with a life-threatening condition. During my period in hospital he was caught by the police drink-driving at excessive speeds twice on the same day. He used my hospital addmission as his defence in court saying he was distressed about my contition.