That is entire plot of 'Ex Machina'.

There are plenty of people that say AI has already displayed a survival instinct, by threatening users if they talk about shutting it down. Or to use a market or blackmail, to get funds to source an external machine to run on.

There are bunch of articles proclaiming AI is trying to break out. Can't find a real study on it.

https://www.wsj.com/opinion/ai-is-learning-to-escape-human-c...