Within the context of the article they mention that rent control leads to overconsumption of housing. In other words, because they keep the rent at below market value people who wouldn’t otherwise rented a home do. This can mean many things, people who would have shared an apartment with a roommate rent by themselves, young people move out of their parent’s homes and rent their own etc... When rent control is abolished prices rise to market value and those people can no longer afford to consume at the rate they previously did. What happens to these people? Well many things can happen, they can get roommates, move back in, move to a less expensive areas, and yes homelessness. So overall the consumption of housing goes down. However, there is little evidence to suggest that rent control prevents homelessness, and that there is a spike in homelessness due to rent control being nixed. Why? Mostly due to rent control causing shortages in housing. This essentially means that even when prices are low due to rent control people will be still be homeless, since the supply of housing is basically null. There are even studies that show that rent control is associated with a high degree of homelessness. On regards of people moving away, I’m not so certain how likely that is. However, I would expect a net gain in people living in an area after rent control is abolished since the supply of housing massively increases.