An interesting topic came up today as I was doing some Christmas shopping. If a customer were to walk in an open door (literally), but the business was closed would you still try to make a sale? I think I might.
Obviously, there might be some caveats. The computer might be down. The cash drawer might be empty. The electrician might have all power off to the building. Believe it or not, I as a potential customer would be very understanding. I might not need a receipt. I might not need change back. I might buy more if I only had a 20 dollar bill in my pocket.
The point is, everyone who walks through the door is a customer. If you are honest with them, they just might understand. They just might be charmed by the unique situation both of you find yourselves in. They might be so charmed by the simple gesture that they tell a friend or two.
The second point is, you don't simple state "we're closed, we're usually open Wednesday through Sunday...". You might not get another opportunity to make a first impression.