Hi Jennifer - I'm with Karen and Ken on this. You won't know until you talk with Glendale Building and Safety Department. Here's a link:
How big a deal it is will vary greatly by area. I helped a neighbor with a similar issue. In my local area, it wasn't a big deal but tedious. It involved bringing the unpermitted area up to code, primarily electrical work But the work and permit costs did run into the thousands so I would try to get a handle on that. I don't know how mortage lenders view unpermitted space so I woud inquire about that, too.
It partly depends on what the space in the basement is - If it is bedrooms that can be more complicated eg 2 methods of legal egress, septic issues if any, etc. The good news is that it doesn't involve an expansion of the footprint and get into other issues such as setbacks and lot coverage.
In my area, it generally would not be a big deal but I would do three things: (1) Talk with the local planning dept and get contractor quotes for the work needed to bring it up to code (2) make sure that my offer included a mortgage contingency in case there is an issue with this and (3) I would talk to my attorney to make sure that I understood legal/title issues if any. (There may be none but I would spend the $200 to make sure.)
Then I would turn around & make it a very big deal with the Seller to negotiate a great price!