I think it automatically deletes messages after 2-3 months, but it seems a bit weird that you'd have 7 messages get deleted at the same time.
In the past I've seen people say that when unread messages get deleted it continues to say you have unread messages even though the messages aren't there anymore.
#Does the inbox empty itself?
scarlet hound
If you're worried someone might have access to your character I would recommend that you unlink any linked accounts here https://jgx.game/MyLinks-
You can check all of your characters for linked accounts on your character management page https://account.runescape.com/game. Any linked accounts will show up to the left of the "Manage" link as "connected" acccounts.
For more security tips https://jgx.game/ja-SecurityTips