Absolutely tell her what is happening in words she can understand. At age 11, they are just getting to understand the meaning of "death". Your daughter should be spoken to in a respectful manner and given fair warning of the symptoms she will see in her friend so she won't be afraid and understand the symptoms are not bizarre things from outer space (if you know what I mean). The better prepared she is now, the better prepared she will be handle her school friend's death/sudden disappearance.
I'm only speaking in how I would feel. My dad died when I was only 6 years old. At that point, I did not get the idea of death. But, I do remember favoring one grandmother's soothing me over another's. I felt comforted by my maternal grandmother who allowed me to cry and stayed near me. And was disappointed when my paternal grandmother took a turn to console me because she would tell me to stop crying and tried to rush me to dry up. I was only 6 but i disctintly remember the difference and it has effected me ever since in terms of which grandmother I feel more close to.