When you have overripe avocados they may not taste as good as if they were just ripe enough but it's very safe to eat overripe avocados and should cause you no sickness.
A lot of people including many Mexican people have eaten many overripe avocados without getting sick from it so you can certainly eat the overripe avocados if you want too.
I've eaten many overripe avocados myself and although they tasted different they never made me sick.
You could also make other dishes such as Guacamole from the overripe avocados where you should not notice the taste difference.