Years ago this was not uncommon. A few years ago I saw a basement that was built in 60's or 70's and and still had not been finished. It has a roof and appeared that people where living in it.

If where you want to built has building codes and requires a certificate of occupancy then most likely not.

Now if this lot leads itself to a walkout basement and you can have full and legal egress. And you will need a permanate kitchen and bathroom, no matter how simple and basic. And you will need to built a permanate roof.

You MIGHT be able to do it.