Thanks for your reply. Would you be able to point me towards a section in the documentation or maybe even a piece of code that handles the killing of the tasks?

I don;t think there is a "kill task" code. By principle, in Linux, as a parent process, ClearML agent launch the training process. When a parent process is terminated, the linux kernel will, in most of the case, kill all child processes, including your training process.
There may be some way to resume a task from ClearML agent when it restart, but I don;t think that is the default behavior

If the agent is the one running the experiment, very likely that your task will be killed.
And when the agent come back, immediately or later, probably nothing will happen. It won't resume ...