When a Eudora POP account ("personality" in Eudora's nomenclature) is imported, the new account is set to have messages go to the Inbox of the account, rather than the global Inbox. Eudora doesn't have an easy setting to do per-account Inboxes (could be done with a filter, though), so almost all Eudora users have the mail for accounts going in to the global Inbox. So when these accounts get imported, they should also be configured to use the global Inbox.
Importing from Eudora was removed from Thunderbird in bug 1243498. Please see http://kb.mozillazine.org/Importing_from_Eudora_-_Thunderbird on how you can still import from Eudora if you need that.