Can I still collect unemployment if I have a sole proprietorship?
The purpose behind unemployment insurance is to provide assistance to workers who become unemployed through no fault of their own. The fact that your business is only breaking even may not really factor into the equation.
Becoming self-employed can be grounds for disqualifying you from benefits--but this can vary depending on state law. So it would make sense to consult with an attorney to get a clear sense of what you can and cannot do in your state.