The correct approach is to use a livenessProbe to check database connectivity and a PreStop lifecycle handler for graceful shutdown. The livenessProbe continuously verifies if the container can connect to the database. If it fails, Kubernetes triggers a restart. Before termination, the PreStop hook executes the shutdown script, ensuring a graceful exit. Option C's PostStart is a one-time check at startup, not ongoing. Option D's initContainer only checks during initialization, not runtime. Option A uses Jobs, which are unrelated to the pod lifecycle. Thus, option B is correct.