The plot is about a moderately successful guitar player and singer Llewyn Davis. That was when he was part of a duo. Then his partner jumps off the George Washington Bridge. That's a loss he can't come back from, despite attempts from others to help him. Also "starter" opportunities come his way. But he kicks them aside. Likely he will remain lost. That's in contrast to the cat he accidentally lets out of the apartment he crashed in who does find his way home.
The cat's name is Ulysses. He's the symbol of resilience, no matter what happens. And that symbol is badly needed today, with so much economic turbulence. Professionals who thought they were set have the rug pulled from under them. College professors lose jobs. Lawyers are working retail. Wall Street folks are driving cabs. Those near retirement may never be able to retire.
Some can halt the downward trajectory. One computer wizard got a promotion. A year later he lost his job. In his early 60s, he hasn't found another. He and his wife are making ends meet through managing property. His identity is coming from doing volunteer whatever with former substance abusers.
More often, those who bumped up against loss mirror the inside of Llewyn Davis. They can't get out of themselves to even search for What's Next. One former BigLaw attorney who came to me for assistance with marketing materials for a small (unsuccessful) law firm he established won't consider making a living at something else. That has been going on long enough to classify him as "lost."
What does Ulysses have that so many other creatures don't? I wish the Coen Brothers focused more on that.