My husband was required to take the week after christmas up through January 2 because the company said they would be closed. He was willing to work, but was not allowed. They told him he either had to use PTO (he only gets 5 days per year) or have the time unpaid. He is a salaried exempt employee. He was not made aware of this closure when he accepted the position. Thank you in advance for any help!

If you search past posts you'll see that this question comes up all the time. There is no law that says that employers have to provide paid time off at all, so employers are free to set restrictions on when/how employees use the paid time off that is provided. If your husband is a non-exempt employee (eligible to receive overtime under FLSA), the company never has to pay him for any time that he doesn't work. If he's an exempt employee, the employer doesn't have to pay him for any week in which he does no work.

While it would have been nice for the employer to have informed him of this policy upfront, there's no law that would require him to do so.

It is absolutely legal to require him to take the time as vacation.

IF the time that the company was closed corresponds exactly to the company's defined work week, then it is also legal to require him to take the time unpaid. If the time the company was closed straddles two work weeks, though, he must be paid, even though the pay can come from his vacation allotment.

Which is yet one more reason to have the work week defined so that it looks like a calendar week. Another reason is that you can go crazy trying to explain the difference between work weeks and calendar weeks to employees.