The US has agreements with a number of third countries to take on non-citizen deportations. According to the article in the link, these include Mexico, El Salvador, Costa Rica, Panama, Guatemala, and South Sudan.

It’s fairly likely that the US applies enough economic pressure until these countries have little choice but to do it. I recall they were trying to force Bahamas and Grenada into it last year, but as far as I’m aware they have managed to maintain their rejection