Extrication is when you set someone or something free. If your dog gets tangled in your neighbor's hammock, she might require some extrication.
The act of getting someone out of a physically tangled or otherwise complicated situation is extrication. When you unwind the yarn your cat is twisted in, that's extrication. And when you get your friend out of a complicated legal situation, that's also extrication. When you get yourself out of a difficult or awkward circumstance, that's also extrication. The Latin root is extricare, from ex, "out," and tricae, "perplexities or hindrances."