Perry,
Once logged in at webmail.verizon.com, go to settings>email settings> under filters, Save Sent Messages you have 2 options to choose from there (save & don't save) if the save option is not selected, then emails are not stored in the sent folder.
Unfortunately there is no way to recover the emails that were not stored, going forward if you select the save option then all emails sent will be saved in the sent folder and you can go in there and delete them from time to time to keep your mail storage quota at a manageable level for your email account.
~STA
Sorry correction on the menu path: go to settings>email settings> under options. (not filters)