Banks are independent institutions and it is a matter for individual banks to say what steps they take to trace the owners of dormant accounts.
As regards banks taking steps to find relatives of a deceased account holder, this raises a number of issues. Banks may not be aware of the death of a customer unless someone tells them. However, I understand that banks do often, due to a variety of circumstances such as the bank/customer relationship, advice from families and from third parties such as payers of pensions etc. become aware when a customer dies. The banks have said that, on becoming aware of the death of a customer, they do endeavour to draw the attention of the next-of-kin to the existence of a bank account.
It would probably be relatively unusual for there to be no documentary evidence among a deceased's personal effects such as a bank statement, receipts, pass books, bank cards etc. which would suggest that an account exists.
Banks also provide a checking service for solicitors or for the personal representatives of deceased persons whereby they can readily obtain information to establish whether or not an account exists in the name of the deceased person. This facility enables the whole of a bank's network to be checked. I should also mention that the banks have recently published an explanatory leaflet entitled "A Guide to Dormant Bank Accounts", together with a claim form, which is available from bank branches. It would be wise for people who have savings or other accounts in credit institutions or other assets to take steps to ensure that their next-of-kin became aware of these assets by leaving a will or some other notification.
On the separate issue of obliging the banks to hand over the assets in dormant accounts to the State, this raises a number of problems. There is no legal definition of a dormant account. Practice in relation to the classification of accounts as dormant varies from institution to institution.