Sorry for my typo, but this sentence should have ended with a question mark "By 'accounts', do you mean deposit accounts, only, or are credit cards, HELOCs and other credit products included, too." We need to establish the type(s) of account(s), because the regulations governing statements (if, when, and how) are not the same for credit products (Reg. Z) and deposit products (Regs. E and DD).
For the sake of discussion, let's say your question relates only to deposit products. The next thing you must determine is whether or not the accounts in question were covered by Reg. E. Since they were enabled with internet banking capabilities, I'll assume that most, if not all, were covered by Reg. E. Accordingly, you turn to Section 1005.9 of Reg. E in order to determine when and how you are required to send a statement. Regardless of your internal policy for declaring accounts (or certain account features) inactive, you must send statements when Reg. E says you must send statements. How you send them is between you and your depositor.
At the time you obtained each e-banking customer's consent to substitute electronic statements for paper statements, you gave him/her a series of disclosures (required by ESIGN) explaining how the e-delivery service will work. Read them. Hopefully, they were worded broadly & spelled out how you will handle termination of e-delivery. If not, now is a good time to have the bank's attorney review and revise your e-delivery service agreements so they DO cover this situation. In particular, if inactivity eventually deactivates your primary statement delivery mechanism, you should spell out the substitute delivery method and any change in service charges that will apply.