This is a little difficult to answer with the information you have provided; however, it is questionable that the homeowner's insurance would cover this unless the homeowner did something to cause the injury - which it doesn't sound like. There may be a claim against your cousin, his company or his worker's compensation insurance company depending on the facts. Depending on how it occurred there may be a negligence case that could be filed - but again I would need more facts to answer this. Considering your husband's injuries I would strongly suggest he not delay in speaking with an Illinois licensed personal injury attorney.
If you were not using a qualified workers' compensation attorney when the claim with the cousin's company was denied, make contact right away to schedule a consultation to determine what can be done at this time.
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With due respect to the other responses, I think your husband's chances are not good. The working for cash is one major problem and that pretty well bars a comp claim. The owner not being there and apparently not directing the means or methods of work takes them out of the chain of people who caused the fall. His only hope might be trying to sue his cousin, but that would require proving that the cousin or one of the other workers actually did something to cause the fall. By that, I mean cutting the branch or moving it, rather than just standing there waiting to clean up the cuttings or watching your husband work. By all means go to a lawyer and talk to him or her, but don't be surprised if this doesn't go the way you'd like it to.
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