An agent needs to have a directory dedicated to Jenkins. Specify the absolute path of this work directory on the agent, such as '/var/jenkins' or 'c:\jenkins'. This should be a path local to the agent machine. Typically, there's no need for this path to be visible from the master.

Agents do not maintain important data (other than active workspaces of projects last built on them), so you can possibly set the agent workspace to a temporary directory if it is ok to lose the latest workspace when the agent is turned off.