You have previously asked for some documents regarding using Markov Chains to perform bruteforce attacks, and I'm still assuming you are looking for techniques to find the low hanging fruits.
There is no obstacles to perform a bruteforce attack using markov chains against passphrases. You just use words instead of characters as states, in what you could call a finite state machine, which a markov chain really is.
Passphrases consisting of random english words. (There are approximately 600.000 of them!, but to be realistic, we only choose 10.000 that would be easy to remember...). This gives a passphrase the entropy of f(n) = 10000 ** n. Comparing a 4 word passphrase to a 8 character long password (using only letters and digits), the passphrase is 45 times harder to crack by pure bruteforce (given the attacker and victim is using the same dictionary).
But, back to the low hanging fruit. Given that a user use sentences rather than random words, the use of markov chain to generate sequence of words, would produce the most likely combination of words that are used to form sentences. Grammar, syntax, stemming and such would all be included.
Given that we have no information about wheter users tend to use random words or sentences for passphrases. It is hard to decide which method would be most effective (dictionary bruteforce or markov chain bruteforce). This is because a markov chain bruteforce probably never will be able to guess a sequence of words that is not included in its training.
Markov Chains are often used in static NLP's.