Does the "Open for extension, closed for modification" principle make any sense?

It looks to me like Bob Martin needed something starting with O to make SOLID and found in some old book this (possibly useless) Open/Closed principle.

How can Open/Closed co-exists with the Single Responsibility, that states a class should have a single reason for change?

If I want to follow Open/Closed in a long living system, am I supposed to have a chain of dozen classes, each extending the previous?