Where would that person in that rent controlled apartment be otherwise? Chances are, on the street. Moving requires upfront capital. It requires promise of a job at the other end. If you are in a high cost of living area like NYC or CA, you might have to quit your job if you want to find a more affordable apartment; there might be absolutely nothing affordable within a three hour drive of your job of cleaning up a downtown office or working a bar, and there may be absolutely no jobs in areas that are affordable. Throw in multiple earners, as is the case of many working poor in overcrowded rent controlled apartments, and you've complicated the problem further and make it even more difficult to wind down your life in one location and wind up in another.
And let's be reasonable here, rent control is not some handout. It's not a subsidy or a tax. The price you pay on your first year in a rent controlled apartment is market rate. Rent control simply says rents cannot go up say, beyond 4% a year. Perfectly reasonable in a world where wages for the working poor rarely go up beyond 4% a year. If landlords want to make more rental income per year, they should instead lobby their city council members to allow them to build more units per parcel, rather than lobby to artificially constrain housing supply with zoning and/or red tape in effort to raise real estate values.