Yes, what you're describing sounds like a classic use case for reverse proxy chaining using HAProxy or SSH tunneling.

Since Server 1 can initiate outbound connections but not accept inbound ones, one approach could be to have it connect to Server 2 via reverse SSH tunnel, and then route external traffic through Server 2 to access services on Server 1.

HAProxy could also be configured on Server 2 to listen for connections and pass them through the tunnel, but you'd need to handle port forwarding carefully and ensure firewalls don’t interfere.

Depending on your use case (web service, internal access, etc.), you might also consider using tools like ngrok or Cloudflare Tunnel for temporary remote access.