A high school teacher in Indianapolis reports her students use the verb finesse to mean "to steal." This is part of a complete episode.
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I'm surprised that you didn't mention the very common use of this verb and that is to finesse a card trick. I know it from Bridge and Euchre. To finesse a card trick is to play a card that will lead to a loss of one trick but sets up the rest of the play to win further tricks or a trick. An example would be in Euchre where you would play a low trump card in hopes of pulling a high trump card that is not in your hand. In this sense of the word it is "stealing" the other tricks.
I'm reminded of the nello bid in 42 dominoes [see Wikipedia 42 (dominoes)] where you bet that you will catch no tricks and thus win.
I remember doing that successfully only once. I was playing against very experienced players who played 42 as if it were their job.