Argentina has had the same problem for decades. Bolivians, Paraguayans and Peruvians have trickled down nonstop since the '60s, maybe even earlier than that. Most of them entered the country illegally.
While renting an Airbnb here, this summer, a carpenter had to come fix the kitchen cabs that the previous renter had broken. This carpenter is from Peru, he entered Argentina illegally in 2001 and became a permanent resident 13 years ago. He said that during the time he was undocumented, the police would stop him often asking for money not to take him to jail. He said that during his first years here, when he was selling cheap stuff on the streets, every Friday police officers would stop by to collect money from all the undocumented vendors. If they didn't have money, the cops would take them to a comisaría.