In article , said...
Aside from the points made by others, no bank/mortgage company will touch a
property which does not have a Certificate of Occupancy on an extension, or
in this case, a finished area. Ask the current owner if he/she is willing
to do the legwork to get the C of O and pay the fines. It can get very
expensive and time consuming. If he/she won't, walk away.

That's not true at all. I sold a house last year with a basement that I
did off the books. I also know many people that have done the same thing
and had no problem. It is quite a common occurrence, legal or not.