Hello! You write that the cable has burned out completely, but you are told that the remnants of the cable do not have any short-circuit traces. You are being misled - there was a short circuit in any case, regardless of the reason why the cable caught fire. In this case, the cable could catch fire due to a short circuit and a failure of protection, which did not disconnect the damaged section - a burnt cable. Protection - a circuit breaker in the metering board from which this cable runs. This protective device must be disconnected in the event of a short circuit on the cable.
Also, the cable could catch fire for another reason, but in the process of burning its insulation, the cores touched, that is, there was a short circuit while the cable was burning. The cable cannot be burnt so that there is no short circuit.
While the cable was burning, the cores were in contact, and if the short circuit was not eliminated (the circuit breaker at the supply substation did not turn off), then the neighbors observed voltage surges. Overvoltage and short circuit are different phenomena. If there were just voltage drops, then there should be no traces of a short circuit. Electrical devices burn out from voltage surges, but this phenomenon should not cause damage to the cable.
Another question is regarding the protection of the cable and wiring in general. If there was an overload and the machine did not turn off as expected, or if the machine was selected incorrectly, then the cable could warm up. Heating the cable can lead to a fire, especially if the cable was laid without additional protection directly over the tree (which is unacceptable from the point of view of fire safety).
Neighbors consume electricity as much as the limit for their house is determined. That is, what kind of introductory machine the representatives of the electric networks put them, this should be. Neighbors should not arbitrarily set consumption limits for themselves. Usually, the machine is installed before the metering device, in a dashboard with a counter. The nominal value of the machine (current) is chosen by the representatives of the email. networks and if more than the set limit (machine current) is turned on in the house, the machine will turn off. Residents cannot arbitrarily increase their limit - that is, set the machine to any current.
If the TV worked, there was no short circuit either in the wiring or in the network. As for power surges, they would not have been noticed on TV. Voltage drops can be seen on ordinary incandescent lamps, on the unstable operation of the refrigerator.
In general, what conclusion can be drawn in a few words:
1.A short circuit somewhere on the line or voltage drops cannot cause a fire
2.This cable should not be laid in wood without additional protection - this could be the main cause of the fire
3.The cable may catch fire due to a short circuit in your wiring, due to a short circuit on the cable itself, due to overload, which did not turn off by the machine due to its malfunction or if it was incorrectly selected.
4. If the cable is completely burnt out, there was a short circuit in any case, regardless of the cause of its fire.
Well, it is also possible that the reason for the fire in the house is completely different. I listed only the assumptions, but what actually happened - I cannot say.
You cannot unreasonably blame the representatives of the electric networks without knowing the exact cause of the fire.