You can view the logs of the previous terminated pod like this:

kubectl logs -p <terminated pod name>

However in most of the cases when there is a problem with configuration or secrets or persistent volumes, running

kubectl describe deployment <deployment name>

Will help debug further.

From kubernetes docs:

Examples

# Return snapshot logs from pod nginx with only one container
kubectl logs nginx

# Return snapshot of previous terminated ruby container logs from pod web-1
kubectl logs -p -c ruby web-1

# Begin streaming the logs of the ruby container in pod web-1
kubectl logs -f -c ruby web-1

# Display only the most recent 20 lines of output in pod nginx
kubectl logs --tail=20 nginx

# Show all logs from pod nginx written in the last hour
kubectl logs --since=1h nginx

Options

 -c, --container="": Print the logs of this container
  -f, --follow[=false]: Specify if the logs should be streamed.
      --limit-bytes=0: Maximum bytes of logs to return. Defaults to no limit.
  -p, --previous[=false]: If true, print the logs for the previous instance of the container in a pod if it exists.
      --since=0: Only return logs newer than a relative duration like 5s, 2m, or 3h. Defaults to all logs. Only one of since-time / since may be used.
      --since-time="": Only return logs after a specific date (RFC3339). Defaults to all logs. Only one of since-time / since may be used.
      --tail=-1: Lines of recent log file to display. Defaults to -1, showing all log lines.
      --timestamps[=false]: Include timestamps on each line in the log output

That is just a simple way of doing it. But in production , I would send all the logs of all the pods to a centeral Log management system such as ELK by deploying a log sending client on the kubernetes cluster as daemon-set such as fluentbit , that will keep sending logs to ELk where I am able to filter things base don the namespace , pod , container , or any other label.

Running kubectl logs -p will fetch logs from existing resources at API level. This means that terminated pods' logs will be unavailable using this command.

As mentioned in other answers, the best way is to have your logs centralized via logging agents or directly pushing these logs into an external service.

Alternatively and given the logging architecture in Kubernetes, you might be able to fetch the logs directly from the log-rotate files in the node hosting the pods. However, this option might depend on the Kubernetes implementation as log files might be deleted when the pod eviction is triggered.