I'm dealing with the same thing except I have two people one is lazy and one is seriously illed. Couple things I've learn so far:
1. It's much harder to fire someone who is lazy which is a trait that is not easy to quantify unless you are willing to let her work fail under your watch
2. You determine how far you want to go helping the sick employee by seeing how grateful he/she is towards you personally
You should check with HR so you dont have to feel it's only you making the decision, and it really isn't.
