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... no chance of their getting caught.
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Yes, it's correct. "Getting caught" is a gerund and acts as a noun that they can possess, hence their getting caught.
Them getting caught is also correct but them acts as a direct object in this case. You could drop them and still have a readable sentence, "...no chance of getting caught", but them just adds more info.
Their getting caught has fallen out of use in American English in favor of them getting caught, but both are still correct. The former gives me a more formal feeling as well, suitable for academics.
Thanks!