Claude (generally, even non Cowork mode) is vulnerable to exfil via their APIs, and Anthropic's response was that you should click the stop button if exfiltration occurs.
This is a good example of the Normalization of Deviance in AI by the way.
See my Claude Pirate research from last October for details:
https://embracethered.com/blog/posts/2025/claude-abusing-net...