Are there any filters listed in: Settings -> Filters ? (Although filters can't delete drafts.)
Do you access your account with an e-mail client (Outlook, Thunderbird, Pocomail, etc), a mobile app (iOS, Android, etc), an e-mail notifier, or any other add-on/tool/web-site/etc connected to your account?
Check: Google Account Settings->Security Tab->Third-party apps with account access. This MAY work as a direct link:
https://myaccount.google.com/u/0/permissions . Have you given account access to any other web-sites or utilities?
Is unroll.me on the list of connected apps?
Please check the Details link below the Inbox (lower/right). What are all the types of account access listed there (posting a screen-shot may best)?