Nope, Not the valve core, the valve stem. One the entire valve stem came out of the inner tube. The other the rubber around the valve stem just began to come loose. I've pulled the stem out entirely myself with a floor pump that the air chuck was old and going bad and didn't release fully when unlocked. That was over a long period of time with many uses while it was bad before I pulled the stem out. But on these other two I was watching they had the small hand pumps that connected directly to the valve. As they pumped frantically for a long time to get air in the tire, they were rocking the pump wildly and I wasn't surprised at all when the tires deflated.

Presta valves are the only ones I've seen this with. Schrader's being larger have a beefier boot going into the tube.