Resistors do not fail on their own burned like that.
The failure of resistors is very uncommon and almost always mechanical in nature. On our products, we see a resistor failure less than 1 in 1 million, all axial resistors are tested on our auto-insertion equipment before being inserted into the PCB during manufacture. Since there are only 5 or 6 axial resistor manufacturers of these types of resistors representing ~95% of resistors manufactured, and we use 4 of them, our results will be the same as everybody else’s.
I do see resistors fail because the designer didn’t do their calculations right, or simply screwed up, but that’s not a resistor failure, it’s a design failure.
In my 45 years in electrical engineering, I have never heard the term octopus used.
[edit: it appears that the term octopus is a home brew or DIY name for a DIY type of curve tracer emulator rather than what the industry uses, which is why I never heard it. ]
Hint… if you monitor the current rather than looking for smoke, you can avoid a whole lot of damage.