In Idaho, unless you are a civil servant or contract employee, you can be laid off for any reason or no reason. Entitlement to unemployment insurance benefits is another issue. You are not entitled if you quit or are fired for cause. Asking to be laid off could be interpreted as a quit, so you might want to rethink that suggestion. Be aware that your employer doesn't want you to get unemployment, because it will be charged to them and their rate could go up, so it is in their interests to lead you into a situation that denies your unemployment.
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This answer is offered as a public service for general information only and may not be relied upon as legal advice.
You need to speak to a lawyer who is familiar with employment law, workers' compensation, and unemployment insurance in Idaho. I would not bank on unemployment as a disability replacement. If you were injured on the job, pursue your worker's comp rights. Don't let the statute of limitation on your claim run. Also, gambling on getting your unemployment by trying to contract your way out of your job is not advisable. If that is the route you intend to go, however, I recommend hiring an attorney who can increase the likelihood that you will get your unemployment.