Receiving an empty box

We have received an empty box from our new neighbors moving in from Japan. What is the meaning of it? How should we react? Should we give something back to them?

Where do you live? Is it a decorative box, or is it apparently a packaging mistake?? There isn't any such custom in Japan...

If it doesn't seem to be decorative, i.e. the box itself is pretty enough to be the present, then that seems odd. It's not a custom I've ever heard of.

Give tehm an empty bottle! Hahaha! Just kidding. I have never heard of such custom in Japan. As mentioned above, if it is not a decorative box, it was a mistake or joke... THough I don't think it was the latter.

The OP writes;
"How should we react? Should we give something back to them?"

How about asking them, "Thanks for the gift you gave us the other day. How should we use that box?" and if you like their explanation, you can give something in return when you have time to spare.

Typically in Japan, a new neighbor is supposed to give small gifts as a means of a simple greeting and self-introduction. This gift is usually something like a tiny towel in a paper box or a small box of tea and cakes. It is not necessary to give gifts in return to these types of gifts, but neighbors typically give little things here and there, such as "I made too much cookies, so I thought you might like some." kind of thing.

Like the other posters, in my 40 odd years of living in Japan as a Japanese and being a Japanese housewife for years, I've never heard of anyone sending an empty box. If it was done on purpose it would be considered rude in Japan. Also the Japanese are huge on wrapping, so if one wants to send a pretty box to add to the interior, the person would usually put that box in another box and then wrap it with pretty paper.