Force majeure or a greater force beyond your control is in every carrier contract or if it isn't then you should not be running with them.
In some cases, sickness can be considered act of God - 30 people getting food poisoning from the T/A buffet is a good example - it affects a lot of people at the same time and by the same cuase. A good lawyer can protect you if you use the Force majeure clause in the contract for a number f different reasons. I know that in some cases things out of my hands, Kidney stones for example, can fall under this and I had could of had a choice of using it.
The following is not legal advice but what I know.
The Carrier's and the shipper's rights are actually limited in what they can do with your property regardless if you are loaded or not. Starting with the contract, you are an independent contractor and not subject to their control while in transit with a load - outside of Hazmat and special cases where regulations and routing take priority. They really can't tow the truck if they want to without your permission, unless there is a real and true abandonment of the load but there has to be solid proof that you refused to deliver it or just gave up - being in the hospital is not abandonment.
But because they, the carrier, has to follow a law called the Uniform Commercial Code which states under §2-615, "failure to deliver goods sold may be excused by an "act of God" if the absence of such act was a basic assumption of the contract, but has made the delivery commercially impracticable" there is more to them calling you up and telling you that they will 'seize' your truck to deliver the load.
In addition, if they demand that you give up control of your property to deliver and actually try to put another driver in your truck to deliver the load, they just committed breech of contract and also made you an employee. By forcing this on you and they have taken control of the situation by removing you from your property (tools of the trade) thus eliminating the contractor status in the agreement between you and the company. As much as this may be disputed with the 'experts' here, when you have specific rules outside the contract that govern the relationship and they are broken, there is no gray areas left for the company (carrier) to hide in - congrats you are now a legal employee and will get back wages and benefits. Just remember FedEx has and is fighting some very similar issues and lost - if they can lose, so can rinikydink carrier with 150 contractors (one comes to mind right now that plays games like this and thinks they can do anything).