Again, most all sick chickens show signs of a problem---before they get sick enough to die without treatment. Signs might be staying away from the rest---staying in a corner, runny nose, coughing, way under weight, etc, etc, etc. Always take a few to watch your chickens actions. Its good to go in the coop at night say once a month with a dim light and feel your chickens---pick them up---check for weight, check for "bugs". The only egg bound chicken I have ever had weighed about twice as much as the rest----she got to where she could not even get on the roost poles.I don't even know if she (the hen that died today) has been laying or not but since we don't know how she died will the eggs be ok from the rest of the flock?
The eggs will be fine.