Sorry, but I simply do not believe this.
I have an extremely detailed knowledge of how benefit fraud is dealt with and the situation you have described does not happen.
Cases of fraud-related overpayment of benefits to claimants living abroad are known as 'Abroad Fraud' within DWP. DWP largely relies on tip-offs to identify Abroad Fraud. DWP does not have access to Border Force data to identify Abroad Fraud, nor can BF data be used in Interviews Under Caution or Prosecutions.
The overwhelming majority of Abroad Fraud is due to claimants claiming Universal Credit or Pension Credit while living overseas (unlike the State Pension, UC and PC are not 'Exportable Benefits').
If Abroad Fraud is suspected then the intelligence (usually a tip-off via the Benefit Fraud Hotline - DWP staff don't have time to go on 'fishing expeditions') is recorded on a Fraud Referral Form which goes to the Abroad Fraud Triage Team. They will look at the claimant profile, the likely amount of fraud and their confidence in the intelligence, and make a decision as to whether an investigation should be started (keep in mind that investigative resources are very limited).
If the case is deemed worthy of investigation then the data is entered into DWP's FRAIMS (Fraud Referral and Intervention Management System). A member of the Abroad Fraud team would then pick up the entry. If a pensioner has a UK bank account and a UK address then avenues for investigation become very limited. Border Force data cannot be used and the investigator would literally have to interview airline staff to get statements that the suspect had travelled on a particular date (airlines don't normally hand over passenger lists to DWP). DWP do not have access to banking transactions when investigating Customer Compliance issues. Facebook/Social Media is one area where unwitting self-incrimination is possible.
Assuming evidence is obtained then a decision would be made as to whether the case would result in a criminal prosecution or whether its a Customer Compliance issue. In the case of failing to report moving overseas then it would be classed as a Customer Compliance issue.
State Pension is not a Sanctionable Benefit so the pension would simply be reset to the level it was at when the pensioner left the UK.
If the overpayment has been substantial then DWP may issue an 'Administrative Penalty' ('Adpen' in DWP-speak). Since 2015 the minimum Adpen is £250 and maximum is £5000. Adpen guidelines set an amount at typically half the overpayment - e.g. if £2000 is overpaid then the Adpen is £1000. £10k+ overpayment would lead to the maximum of £5k Adpen. An Adpen is essentially voluntary and the customer must agree to pay it. It cannot be simply deducted from pension payments. If the customer does not accept the Adpen then DWP can prosecute for the amount of the Adpen. However CPS set quite a high threshold on prosecution and where an individual is living overseas the offence would need to be of such gravity as to potentially attract at least a 12 month jail sentence.
The total amount of state pension fraud (UK and overseas) is thought to be very very low - I think in 2022 the estimate was 0.7% of benefit fraud.
The avenues open to DWP for investigating Abroad Fraud by State Pension claimants are really very limited. Moreover the amount of overpayment is invariably small in comparison to other benefit frauds so the cost-benefit of investigation in unfavourable. Almost all cases would be self-incrimination and tip offs due to family/friend fall-outs. State pension fraud is bottom of DWPs priorities. In contrast, for the last Financial Year End about 12% of Universal Credit claims were estimated to be 'in overpayment' (a loss to DWP of about £6.5 billion) - that is over ten times the total estimated cost of unfreezing all pensions (£600M).