LA Worker's Compensation Ins question

[ccm]

I am about to hire a small landscaping company to remove a tree (25' tall) from my back yard. They have liability insurance but do not have worker's compensation. I am an individual and they have employees. It has always been my understanding that if an employer does not have worker comp insurance, the employer is responsible for any employee injury/disability, while on the job. My concern is what happens if the employer does not have deep enough pockets to cover the cost of the injury or disability. Would I then become responsible?

Thanks in advance for your advice.

Charlie