The 6/6 means other configuration change if you look at the RFC.
The (cease) is when the remote peer has an administratively shutdown. I already get it in production, so I made a test to be sure.
With two Cisco router you do not have the notification. But if you deactivate the bgp neighbor on a Juniper you have :
*Mar 1 00:14:41.363: BGP: 192.168.1.2 rcv message type 3, length (excl. header) 2
*Mar 1 00:14:41.363: %BGP-3-NOTIFICATION: received from neighbor 192.168.1.2 6/3 (cease) 0 bytes
*Mar 1 00:14:41.367: BGP: 192.168.1.2 went from Established to Closing
I have a 6/3 so it seem the Juniper correctly send the notification. Do you now what device is in front of yours ?