Yes, you can file a third-party claim for damages if a third party other than your employer was at fault for your slip and fall event that left you hurt. You may be able to file a third-party liability claim against the person or business responsible for maintaining the property where you work or their insurance provider if they permitted a hazardous condition to exist without properly advising the public of such a hazard and you were hurt as a result of that condition. Examples of such parties include cleaning companies.