A friend was born in Mexico and came to America when he was a few years old. He is here legally; has a SSN issued in his name, has a valid driver's license, pays taxes, etc.

Last year he was arrested on grounds of violating his probation. After about 2.5-3 months in jail, the judge found him not guilty of violating but he wasn't released as they said immigration was investigating him. He was held for another 4 months and at his immigration hearing, they realized they had the right name but the wrong person, told him that he was eligible to receive his citizenship, and he was released. Last week, he was arrested and is being told that, once again, he is being investigated by immigration and now, his hearing is going to be in Chicago instead of Milwaukee.

Is there something that he can do at this point? Shouldn't the state be liable for holding him for 4 months without cause when they made a mistake on their end?

You don't say why he was arrested. Is it strictly for immigration, or something else?
He obviously needs a good lawyer, and he also needs to stay out of trouble.
He must have the same name AND birth date as someone else, not uncommon if he has a common name.

You don't say why he was arrested. Is it strictly for immigration, or something else?
He obviously needs a good lawyer, and he also needs to stay out of trouble.
He must have the exact same name AND birth date as someone else, not uncommon if he has a common name.

The local police arrested 7+ "foreign-born gang members" which he is not.

The name is the same, the birth date is different and that's how they figured out back in May that they had the wrong guy.

A lawyer would have had him out of jail long before 4 months were up. He needs to save for one now. I doubt that he will get restitution for those 4 months, but he can try. (We don't know if he is just extremely unlucky or if he hangs out with the wrong crowd.)