Firstly, the personal representatives should not even acknowledge the correspondence until they have sought expert legal advice. Any professional advisor would need to see all related documentation before providing advice.
Even if all of the assets of the estate have been distributed, the bank could go after the beneficiaries if it has a valid claim. An advertisement for claims would have relieved the personal representatives from being personally sued by the bank, but would not relieve the beneficiaries.
The biggest issue is the Statute of Limitations. The bank would have the lesser of six years from the date of demand or two years from the date of death to issue proceedings against the estate, otherwise the bank's demand would be statute barred.
Some loan documents may provide that a non-payment constitutes a breach, meaning that a demand should have been made at that time. Accordingly, a careful review of the loan documentation may be required.
If the bank is not outside the Statute of Limitations, then the personal representatives will need to look at possible defences e,g, were there any major changes to the loan facilities in the last 8 years that prejudiced the guarantor etc.
Another issue to consider is why the deceased left such a large issue "hanging out there". What indemnities did he receive from the purchaser etc.
Jim Stafford