What would be the behavior of a multi node kubernetes cluster if it only has a single master node and if the node goes down?
The control plane would be unavailable. Existing pods would continue to run, however calls to the API wouldn't work, so you wouldn't be able to make any changes to the state of the system. Additionally self-repair systems like pods being restarted on failure would not happen since that functionality lives in the control plane as well.
You wouldn't be able to create or query kubernetes objects(pods, deployments etc) since the required control plane components(api-server and etcd) are not running.
Existing pods on the worker nodes will keep running. If a pod crashes, kubelet on that node would restart it as well.
If worker node goes down while master is down, even the pods created by a controllers like deployment/replicaset won't be re-scheduled to different node since controller-manager(control plane component) is not running.