Bic created their own unique retraction system for pens. This uses a plastic latch which stops the push button from springing open when the pen is in use.
Here is a picture of the internals of a Bic BU2 Grip pen - showing the two plastic parts that make up the button and latch. The refill has a spring that pushes on the button and allows the latch to operate.
I believe that the same mechanism is used in the classic Bic M10 Clic type ballpoint pens. You can extract the push button and latch by pressing the protruding part of the latch into the body of the pen. If you push far enough the button will come free from the pen body. To reassemble the pen, put the latch into the correct position inside the push button, and push it into the pen until it engages with the slot in the pen body.
The sketch shows how the latch uperates.
What is nice about the Bic mechanism is that it relies on the springiness of plastic!