Short answer
HubSpot's KB: conversations sit in views grouped by assignee, channel or status. An outgoing email sent from the inbox doesn't appear in All open until the contact replies. Use search with a date filter to find older threads.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Check the view first when someone says a conversation vanished.
3. Related
Custom inbox views and inbox channels.