"overheated coil in the induction motor….is there any posibility the copper also heated and can cause to the failure"
You didn't exactly say it but I'm assuming there was a stator failure resulting in motor trip? Are there any more details about the failure scenario and visual observation of stator failure location. How about bridge test? Surge test? Stator core test (thermography and watts loss)?
Some possible links between apparent overheating of rotor and damaged stator coil:
1 - Rotor rubbed stator bore. This caused friction heating of both. Also smeared the stator laminations creating eddy heating of the stator core. Localized heat contributed to stator coil failure.
2 - Damaged stator coil continued to operate for some period but creating severe unbalance in stator field, creating reverse rotating field which is 120hz, cause deep bar heating of rotor (don't know exactly how big this motor is).
3 - Attempts to restart motor with damaged stator might also have similar effect.
4 - Rotor bows in response to heating from stator fault (and resulting heating from effect 2) and causes rotor bow. But in that case I'd normally expect rub at one arc of circumference of rotor and all around stator...doesn't seem to be what you've got.
5 - Stator failure unrelated to visual observations shown. Example maybe there was a rotor/stator that occurred years ago and you only notice it now that you tear everything down after the stator failure. It doesn't seem particularly like that they are unrelated, but I don't think you'd be able to rule it out with complete 100% certainty unless / until you can examine the area of the stator failure closely.
Since you included photos the ID of stator bore I gather maybe you're focusing on scenario 1. I tend to agree for what little it's worth from a distance, but you have much better info available to you there. End ring distress may be rub marks. On stator there appear to be rub marks primarily at the near end at bottom of photo. If worst stator bore marks are on the same end as worst rotor marks, it might tend to explain why the rotor heating is concentrated at one end and corroborate the scenario 1. In that case there is some more thinking to do about how it happened (bearing holding rotor off-center within stator at one end seems most likely but there may be other possibilities)
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(2B)+(2B)' ?