I am contemplating resigning from my current position for several reasons and I wanted to know if I would be eligible for an advance bonus or some sort of other compensation if I did so. I work in the private sector and one of my colleagues was recently fired for performance issues.....so basically, I was doing all the department work. The individual received a severance package and my workload continued to increase. Does the termination of this persons employment give me any compensation leverage if I quit?

Not under the law, no. It would depend on company policy.