Meaning of wolves crossing city street in Collateral

It's not a wolf or a fox, it's a coyote.

There is none, it was a happy accident (as mentioned on the movie's wiki page):

One event of note was the filming of the coyotes running across the road; the low-light capability allowed Mann to spontaneously film the animals that just happened to pass, without having to set up lighting for the shot.

Entertainment Weekly theorizes:

There is a metaphorical animal, a coyote crossing the road. This is all in the lead-up to the Korean Nightclub scene, a sequence that is by far the best-known scene in Collateral. It's a bad omen, but it's also bizarrely optimistic: a reminder that none of this really matters, that Los Angeles is still a desert underneath all the palm trees lit up black by the High-Def video. On the soundtrack, Cornell sings, "I can tell you why people die alone." In the hospital Max visits every day in Los Angeles, his mother appears to be in the process of eternally dying. Vincent kills people and feels nothing; ultimately, Vincent winds up dead. The Symbolic Coyote is probably the least troubled character in the film.

I think it was a little bit of a revelation to both of them.

As the wolf/coyote walked by they both looked at each other, Max looking at Vincent as the lone wolf out there at night and sort of looking at him in awe wishing to be somewhat like him in a way.

Also Vincent looking at the wolf realizing for the first time that he is alone and not reaching the place he wants to be in life and looking at Max and maybe being jealous or in awe of Max.

Either way I love that Mann put that in the movie because you can come to whatever realization you want with it and its still a great movie!!

The EW theory is dead wrong. First of all, it's a wolf stalking a coyote; not two coyotes. Secondly, the coyote is in no way "the least troubled character in the film." It's running for its life.

The wolf represents Vincent and the coyote represents Max. Max is starting to put together the fact that Vincent is setting him up, as es evidenced by his repeatedly asking, "Why didn't you kill me and find another cab driver?" Vincent sees himself in the wolf, too -- a lone predator stalking it's prey in the darkness. His dialogue with Max, advising him to follow up on his date if he survives the night, is a sign that he has felt the loneliness of his "lone wolf" lifestyle. Both men and both animals are out of their natural element and the two men are starting to realize that they need a change in their lives.

To be honest there's some truth in all of these answers although the entertainment weekly one is obviously wrong. it did point out an important part that plays with the wolf and coyote scene. Which is the Korean night club scene. During which, Vincent saves Max's life and then stares at him intently as if to tell him "we're in this together". Right before this, he told his mom he was thinking of him as a friend. What came after, was Max showing how angry he was by tossing the briefcase, and Vincent putting Max to a test in which he passed. The symbolism with the wolf and coyote is Max seeing that he is basically being stalked. Vincent seeing what his whole life has been about.

Vincent is ex military and an assassin. His life had been about death. Surely any "friends" he had made has died. Or he killed them. Meeting Max he slowly softens and sees his life has no end. He tells Max about his dad, he jokes with Max, he offers advice. Vincent I believe is having issues with his own demons and it shows when he saves Max's life. Vincent saw the police and knew that they were both screwed at that point. It would have been best for him, to let Max die and carry on by himself. He didn't want to do that anymore I guess.

It's a great tie-in scene. To have that wolf chasing the coyote through the night. Also, later when Max tells him how he really feels by putting that question to him "tell me what's going on in your head" etc. You can see that Vincent is hurt by what Max is saying. Would a lifelong murderous cold deadly assassin ever have his feelings hurt? I think he was changing and knew it by the end that Max had changed him. He welcomed death

The most interesting thing about this scene I think is not the wolf crossing the road but the the cut scene to the advertisement on the roof of the cab as the cab drives off. Check it out! It says "Silver". Seriously check it out.

Is the symbolism here that wolf is chasing the coyote. And then Max is the Coyote and Vincent is the wolf but Max has the "Silver" Bullet or the Cab, to kill the wolf.. A little foreshadowing maybe...

I know I know its a long shot but this scene I believe is one of the greatest scenes in a movie. The music, the atmosphere, the use of nature.. The way it slows the movie down for the audience to catch a breathe and see the real world through both Vincent and Max's eyes.. I love it.

Vincent killed people for a living. He exterminated life. He was a very damaged character, he didn't really care if he lived or died. He had to be like that. He knew any day could be his last, that was his reality. Overthinking was his defense mechanism (from being human). He thought about oblivion, and he ran there anytime he might have struggled with his lifestyle. I believe Max's talk about escaping to his happy place earlier in the movie has something to do with it. The most obvious being- In oblivion, nothing matters. That was Vincent's escape.

Understanding that is important because that was his conflict. We can speculate on his past, but what we do know is he did not seem to mind killing people. In order to be like that, you would have to view people as you would bugs. Inferior and meaningless (for most people). But that would also mean you look at yourself as a bug, in a sense. Also, the only people Vincent interacted with were probably crime lords and killers, therefore reaffirming his stance on people being bugs and solidified his disposition. A place like LA pretty much represented the epitome of that mindset, in a bad way, as he referenced the people being disconnected from each other. That would mean that there was still a piece of him that did not like his "happy place".

But then, here comes Max.

Vincent had this idea that people didn't care about each other, and in his world that was probably true. But Max was a people person. He wanted to cater to people. He wanted to make people feel good. His idea for his company reflected that, a experience so good that you wouldn't want it to end (the limo ride). He visited his dying mother everyday. He had a conscious. Vincent, being the intelligent man he was, could recognize those traits in him. He started to see Max as human, not a bug.

The coyotes represented a few things. First, survival and adaptability. In the middle of this huge concrete jungle full of people, two "wild" animals you wouldn't really expect to see, predators, are defying the odds. They are surrounded by bigger threats than what they pose- and yet they are adapting and surviving, independent from domestication. Also, coyotes are sneaky. They can stay hidden pretty well when they want to. Their intuition is strong, and they usually avoid people. But, in the middle of driving, Max spotted them. Perhaps they showed themselves, as they say animals can sense things about people. Another important note is that Max actually stopped for them. How many people would have? Whether it was to insure their safety crossing the street, or to just watch them- Max made a point to do it. Even in the middle of all the chaos he was in middle of. That was his nature. Vincent recognized that. I think that's when Vincent had it in his mind that Max was probably the one guy in this world that he did not want to kill. I think even at the end, when he was dying and he asked Max if anybody would notice a man dying- what he was really asking was for Max to remember him...to notice him, that he actually existed as he spent much time "not existing". Hiding in the dark, like those coyotes. Just as Max shined some light on them, exposing them, he would do the same for Vincent. He would see him for who he really was, even if it was just him that ever would. And knowing that, in his final moment of life, was Vincent's ultimate "happy place".