never heard someone staying in basements . try criaglist you might find. but ingeneral the studios and apartemnts in waukegan or near chicago which are pretty cheap. so if u just wanna stay in a basment to save some money then you could also consider these cheap studios.
I went to a few places in Waukegan and Gurnee. So if you need any info, I can give my 2 cents. But before you live somewhere, def go check it out first or have someone else. I dont really know anything about basements though. But I found a classifieds page from Gurnee area which has rooms and other unknown things around the area. Might help, might not.
There is a subsidized apartment complex in Gurnee that is really nice; it's mixed in with townhomes in a residential area right by all of Gurnee's shopping and what not, but I don't remember the name of the place. I'll try to make a few calls today to find out. There is probably a waiting list though.