When an update leaves the system broken.
FIRST
If you took a snapshot before the update, restore it. That is why you took it, and it is faster than diagnosing.
IF YOU DID NOT
Identify what broke. Check service status and logs for the affected services.
COMMON FAILURES
A configuration file replaced by the package, losing your customisations. The old version is usually saved with a suffix; compare and merge. A deprecated option causing a service to refuse to start. The log names it. A dependency conflict leaving packages half-configured. The package manager usually offers a repair command. A kernel update leaving the system unbootable. Boot an older kernel from the console boot menu.
USING THE CONSOLE
If the system does not boot or SSH does not start, the provider console is your access. Every VPS should have one, and knowing how to reach it before you need it is worth five minutes.
PREVENTING IT
Snapshot before updates Update at a time you can deal with a problem Read release notes for major version upgrades Test major upgrades on a test server first