Yes, you can make a living off a part-time job. Typically it won't be a luxurious living, but many people pay their bills with jobs considered part-time positions.
For example, landscapers, realtors, and web developers work flexible hours but can earn a livable wage, and many bloggers, document translators, and market research analysts do the same.
How much you earn will depend greatly on where you live, as if there is little to no demand for someone in your field in your area, you'll have a harder time making a living than you would somewhere where there is high demand.
Before you quit your job to jump into a part-time gig, it's important to note that it typically takes at least a year or two to gain experience and build credibility to begin making good money from many of these jobs. Most of these positions earn livable wages by building a solid client base, which takes time and energy.
It's best to assume you will make little to no money the first year or two you work part-time unless you join another company that offers you a guaranteed paycheck. However, the downside to those is that they usually don't pay as much as many freelance-style roles can.
