No. Your only avenue is through workers’ compensation. It is possible in some instances to get an additional 10% penalty against your employer if you can prove that they willfully failed to comply with any statutory requirement. While the law doesn’t specifically state, this it is generally understood to refer to a safety statute.
In practice, we have seen the Industrial Commission enforce this law very, very rarely. Understand that “willful failure” is a high standard to meet. That is far more serious that “should have known” or even “stupidity” and “reckless behavior.”
The only exception to this is if your employer was required by law to carry workers’ compensation insurance and failed to do so. The employer cannot then claim the Workers’ Compensation Act as a defense in a lawsuit. As a practical matter, this comes up most often in the construction industry.
