Invariably it is from someone who is using more than one device for receiving e-mails, I-pod, Smartphone, Android or simply another newer computer, whilst still using the old one.
Your old computer will have been set up to receive e-mails using POP or IMAP settings.
These will override your newer device and/or webmail settings. The result is that when you switch on your old computer, and open your e-mails in Outlook or Windows Mail, it “Pulls down” all your e-mails from your other device(s). You can still read and deal with them on your old computer but unfortunately they have gone from your new device forever.
What you can do is open a new webmail account on your old computer to access your e-mails from there on, not your old ones, but be sure not to open Outlook or Windows mail or you will pull them all down again.
All email programs have a setting to allow you to decide whether you wish to leave your messages on the server after you have downloaded them, and how long to leave them there. If you are very clever, (beware) If you wish to use POP login some of the time and Webmail or IMAP login some of the time, you should locate the setting (usually found on the advanced email settings page) in your email software for ALL POP logins you have setup, and set it to leave your emails on the server for say 30 days. The setting is usually called something like “leave a copy of messages on the server” or “keep messages on the server”.
Unfortunately there is nothing that can be done do to put back the messages that your email software has already deleted, but if you change your email program settings as above your new emails will stay in Webmail for the period you set.