At IBM we had a Customer Relations department what we called Critical Situations or Crit-Sits. Generally one software issue didn't make a crit-sit. Generally most had 2 or more serious issues requiring escalation that needed to be addressed.
Initially critical-situations were handled through this team. As CS developed. The crit-sit was opened through the system but the CSM ran the crit-sit. Additionally,, if it hadn't been yet escalated a CS could open a proactive situation which wouldn't receive as much executive attention but would alert development teams to the problems the customer was experiencing so they could ensure that they were working the issue.