If a private investigator has enough information to search for that person then yes sometimes a private investigator is able to find out where someone actually lives.
It's kind of scary to think about but even you or I could find out someone's address and other personal details online through online people search and background check websites.
All we need is the age of the person and their name and possible address and once we pay a fee of around $5.00 to $10.00 we can get all the information of someone including, current address, past addresses, phone number, any criminal records etc.
Most times a private investigator is just interested in what the person is doing and not really caring about where they live but if someone hired the private investigator and wants them to try and find the address of the person then it's sometimes possible for the private investigator to find out where someone lives.