Your BFA can get you internships and apprenticeships offered in your BFA's field of study/Concentration. Rely on your skill sets to hone your arts trade--framing, art handling, sign painting, graphic design, printshop, etc.--while supporting your life expenses and artistic direction.
I hope to have shed some light on your question.
There are many jobs you can get with a BFA (art director, graphic designer, teacher, producer etc) not all art careers require one but it might be advantageous to have one. It all depends on what area of art you would like to specialize in, painting, digital arts, photography, film, fiber arts, ceramics/sculpture etc. All of those career paths can lead to different jobs. Some majors you will be more likely to be a freelancer than in a full time position with one company. I would think about what area you would like to pursue and look at careers in that specialty to see what is available. Having a BFA could allow you to teach art as far as I know most colleges require a masters degree. I can't answer how many career paths are in the broad spectrum of Art but for me I have a BFA specializing in photography and I work as a staff photographer full time for a photo agency but I also freelance. My career path by no means requires a BFA but I have found that my education has helped propel me forward. I hope this helps a little, if you have any specific questions I can do my best to answer those as well.