What happens when you are asked to place item in the hold (checked-in) luggage?

I have an international flight out of a USA airport recently and I've never been through one before (on the way out that is) so this is a question whose answer is not immediately obvious to me.

I 've never been asked to place any items found in my carry-on luggage with the hold luggage, but I am wondering how would that work in practice? In all international airports I've traveled from, you typically hand over you hold luggage during check-in so by the time you reach the baggage screening area you don't have it with you.

So, if you are asked to place something with the hold luggage, what exactly happens? Do you go back to the check-in counter, wait in the queue a second time, and then ask them to please bring out your luggage as you have something more you need to add to it? Or is your entire carry-on baggage placed into the hold? What if you only travel with hold luggage and a backpack or some other bag (e.g. notebook bag) that cannot be placed with the hold luggage?

The item(s) in question are mechanical keyboards so I'll be set back a few hundreds of USD if the only option at that point is to discard them. I've asked a related question and at least of the answers I received indicates that there is a (slim) possibility I may be asked to check them in, hence this question.