For internal cable wiring material, the insulation material was either PVC (polyvinyl chloride) or rubber.
PVC contains heaps of chlorine attached chemically to the base plastic.
With rubber, this material was traditionally 'cross-linked' with sulphur.
Over time, the insulation material reacts with the metal (copper), and produces a copper salt. In the case of PVC the green salt is copper chloride. With rubber, there is a more insidious reaction. The sulphur used in the cross linking, reacts against copper to produce copper sulphide in the heat reaction of the cross linking. To protect the copper against reacting with the sulphur, it was traditionally coated with tin. There was no reaction between tin and sulphur, so everything was OK. BUT, over time, there is an inter-metallic reaction between the tin and the copper. Compounds of tin/copper form, and these are further oxidised to another tin/copper compound, neither of which are very good conductors of electricity.
So over time, the copper conductor develops a higher and higher resistance. The problem is worse with fine multi-strand conductors, as you note.
The modern PVC insulations are generally better than older formulations but still, the use of PVC is not liked by cable people. PVC is a complex formulation and includes a plasticiser and this is generally fairly volatile, so after time, the insulation goes hard and cracks. A low temperature PVC material is quite expensive, and other materials are often used nowadays. But cheap commercial insulations are just that;cheap. They will harden, corrode, and embrittle, in short time. High temperatures accelerate the process.
PVC is popular because it is cheap. But increasingly, commercial use of insulated conductor cable is calling for halogen free materials.