No, everyone just sleeps on the street. They don't have to own a house but they gotta have a place to sleep and in NYC that equals a massive number of hotels accommodate all the tourists and apartments for the residents.
Like I said you don't have to be able to talk to all of the NPC's but they need have a place to sleep, possessions and purpose whether that be a job or some other reason for being in town such as trade or personal business.
Giving someone something to do - a reason to exist - is really, really easy to do procedurally. In the simpliest case, you can just pick from a list of items, filtering out those which aren't applicable to that NPC:
* Looking for a job as [one of jobs available based on skill levels]
* Visiting [one of other NPCs marked as "friend" who owns a residence in town]
* Visiting own family [one of the residences marked as belonging to an NPC who is marked as "family"]
* Working at [one of the workplaces with skill requirements fitting the skill levels]
* Visiting [one of pilgrimage or tourist sites in town]
* Waiting for an audience with [one of the potentates in town]
* Looking to join [one of the guilds available based on skill levels]
* Shopping at [one of the speciality shops in town]
* Trying to sell [wares based on current job, if the job is a "producing" one]
* Spying for [one of other powers/towns]
* Planning a revolution
* Trying to get drunk, laid and entertained, not necessary in that order
* Passing through on the way to [one of the other places which this town is a possible passing point for]
* Looking for a spouse
* Looking for a missing [one other NPC marked as "friend" or "relative" to this NPC, which the story engine decided to set up as "missing"]
... and possibly quite a few more.