My S -pen also broke. When I popped it out it went flying behind me. I found all the pieces, or so I thought. Going to a Verizon store was no help. Calling Verizon was no help. Finally I called Samsung and they told me to return it to them for replacement. Then I was in the Verizon store again and this time the rep. told me NOT to send it back to Samsung-that I'd get a refurbished one as replacement. Then the rep. smacked the phone down on his open palm and the (whole) pen dropped out. The force of the jolt when the phone hits the hand pops the pen out - at least partially. Just make sure the pen opening is extended out from the hand. Don't use a table or any other place that is hard.
The rep. suggested that I contact Samsung again and ask for a replacement stylus instead of replacement phone. The stylus had broken at the only "seam" on it and when it did, the spring was lost. Without the spring, the pop-out doesn't happen.
Hope that helps.