Proactive Web Messaging notification fails for closed sessions

Trying to trigger a proactive notification for a customer who closed their browser tab. The session ID is still valid in our DB, but the API call fails immediately.

POST /api/v2/conversations/message/{conversationId}/events
{
 "event": "outbound",
 "to": "user:123",
 "text": "Are you still there?"
}

Returns 400 Bad Request with “Invalid participant state”. The doc says outbound events work on active sessions, but it’s not clear if ‘closed’ counts. Is there a specific API to reopen the session first or am I just stuck?