Yes, they can often be recovered if they were moved rather than permanently removed.
Try these checks in Outlook.com, in this order:
- Check Deleted Items
- If the missing messages are there, select them and choose Restore.
- If they are not there, open Deleted Items and select Recover items deleted from this folder.
- Messages removed from Deleted Items are recoverable for 30 days.
- Check Archive
- If the emails were archived, they will not appear in Inbox.
- Open Archive, select the message, then choose Move to > Inbox.
- Check Junk Email
- Sometimes messages are incorrectly marked as junk.
- If found there, select the message and choose Report > Not junk.
- Messages in Junk Email are automatically removed after 30 days and are not recoverable after that.
- Check Focused Inbox / Other
- If Focused Inbox is enabled, older messages may be under the Other tab.
- If found there, select the message and choose Move to > Move to Focused inbox.
- Check the Filter setting
- Above the message list, select Filter and set it to All so older messages are not hidden by a filter.
- Check Rules
- A rule or Sweep rule may have moved messages out of Inbox.
- On a computer, go to Rules settings and review any rule that moves or deletes mail.
- If unauthorized access is suspected
- Review the account’s Recent activity page to see sign-ins from the last 30 days.
If the messages do not appear in Deleted Items, Recover items deleted from this folder, Archive, Junk Email, or Other, then recovery is unlikely from Outlook.com.