A typical house circuit breaker is 15A or 20A, and often feeds several wall outlets. In my experience, most household three-prong extension cords are rated for 12A or 13A. To a layman, they would likely look indistinguishable from an actual heavy-duty extension cord, which would be rated for at least 15A. (It is certainly possible to find one of these, but they are typically more expensive and harder to find. You’d likely have to specifically be looking for a cord that is rated for 15A.)
So it is certainly possible to overload a three-pronged extension cord and not trip the circuit breaker. The easiest way to overload an extension cord is to put multiple high-power devices on one cord, which is why it is generally a bad idea to connect a power strip to an extension cord.
In particular, it is very easy to inadvertently connect a 15A power strip to a 12A or 13A extension cord. This might not be big deal if it’s just a few low-power electronic devices on the power strip (like cell phone chargers), but can be a real problem if connecting high-power devices with heating elements to to the power strip.
In the setup the OP is describing, I’d be particularly concerned. The outlet circuit breaker is not tripping. The power strip is tripping, which is good. But nothing is protecting the extension cord, which is hot to the touch. This could quite easily result in a very dangerous situation, like a possible electrical fire.