It's more like "what if you hired a moving company and, halfway through, one of the guys comes down with a bug and starts puking?" in which case I'd say he should go home and hopefully his employer pays him for his time off because unlike people like you I do think people should be paid even when they're sick, to a reasonable degree. Also I don't want to get sick so if you're sick please stay home!
I would also tell him to go home but I wouldn't be paying full price for it. I would arrange them to finish the job the next day if they want full payment. If you still pay them, you are paying for a sub standard service.
How DARE they have pay people that spend almost every single day of their lives for years when they're sick?
How dare you force people to pay for a missing days worth of productivity (which you agreed upon)?