Kubernetes rollbacks also have a mechanism to keep previous versions of deployments. Even if a new deployment doesn't pass through health checks, you could very easily roll back to a previous version using the kubectl rollout undo command. This is how you would do it.
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By defining readinessProbes and livenessProbes in your deployment YAML, you can prevent unready deployments from impacting the live service and ensure they can be rolled back quickly if necessary.