It seems that if the employee is put out of work at no fault of their own, they should still get paid.
Should isn't the same as "has to."
The doctrine for employment law in most areas of the US is "at will" employment. Either party can legally terminate employment at any time and that is (with specific exceptions) generally held to not be a basis for legal actions.
Layoffs tend to follow exactly the same principle. Many companies have temporary layoffs due to business conditions, and, for renovations. It's not only legal but it is widely practiced in manufacturing type fields.
Being hourly or salaried has little to do with it. If your employer has no work available for you, they can dismiss you, permanently or temporarily.
Where the law enters into this is unemployment eligibility. When an employee has exceeded a certain number of months of continuous employment and earns over a certain amount on average per time period, their state will consider them eligible for unemployment payments during a layoff, temporary or permanent. Part of the unemployment payment comes from the most recent employer. So you'd have to pay a part of your employee's unemployment payment during a temporary layoff. That is where the law applies to the employer.
There are also the following conditions - edge cases - that affect layoffs.
There is a national law that says that an employer of a certain size (number of employees) who has to make permanent layoffs of a certain number must pre-announce the layoffs publicly. This applies to employers laying off hundreds of employees. I do not know the specific laws. Since that is probably not the case here I'm not going to look it up.
Secondly, if you fire someone for cause, many jurisdictions disallow the person from collecting unemployment payments. I have witnessed a few employers treat a layoff like a firing in order to not have to affect their unemployment payments. When it is a group of, say, 10 or more employees who are "fired", that can be successfully contested and it looks like a layoff. Now, this is sleazy, but I have witnessed it attempted.
The bottom line to answer your question: normally almost never, at the vast majority of companies. The exceptions (businesses that do cover payroll while employees are furloughed) get written up in the business press as extremely generous.
Should employees get paid during a shutdown? Depends on the situation and how irreplaceable the affected employees are and how much money is available. You should determine your unemployment burden if you do a temporary layoff. That's normally what is done.
Also if practical, look for creative solutions like renting a temporary office or work-from-home that justifies keeping people on the payroll.