Swelkie
Your son's ESA will not run out in November!
ESA is an indefinite award and will only stop if a Fit for Work Decision is made and this requires a face to face assessment to have been done first.
If you have a letter with a date for the beginning of the month then this is an administrative date concerned with the Christmas Bonus and is not related to the claim ending.
If you want to find out when your son's claim is due for renewal then he should contact the DWP office dealing with his claim.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems