Can the detainees simply leave the American camps?

By American Camps, I am referring to the centers where foreigners are currently detained. I am trying to avoid the political descriptors that are sometimes used to describe these places.

I am also NOT taking a position with regard as to whether these people should or should not leave.

I am only asking if they could decide to leave (presumably with an additional obligation to leave the country). Would the detainees be allowed to?

I ask because I am aware of a report that a politician had said that the detained kids could leave at any time, and I’m uncertain of the facts.

Thanks in advance.

There is an immigration policy known as “voluntary departure”, but it is not as easy as just walking out the gate: