Flameduck: Why on earth wouldn't you ask the ISP to close the mailbox if you never intend to use it anymore?
Leaving it open only wastes their resources, and can thereby have a (tiny) negative impact on your 'good' account on their servers. Plus people that genuinely try to reach you would be under the mistaken impression that you'd received their message without the rejection notice (until you run out of space, but even then -- a "mailbox full" error looks temporary, "mailbox not found" is somewhat more permanent)
Leaving it open only wastes their resources, and can thereby have a (tiny) negative impact on your 'good' account on their servers. Plus people that genuinely try to reach you would be under the mistaken impression that you'd received their message without the rejection notice (until you run out of space, but even then -- a "mailbox full" error looks temporary, "mailbox not found" is somewhat more permanent)