When my father died, I reset the password on his email account (it was running on the family domain, which I administer) which made it easy to discover and close various online accounts, find contact details for people we thought should be invited to the funeral, and generally find out more about things we knew existed, but didn't know much about.
We didn't go through gigabytes of data, but searched (it's GMail).
I haven't thought to close the account, and I don't know if my mum still has reason to access it, but since it's costing me nothing and I never notice it it will probably be around for a while.