If the piece is small just get rid of it.

The last thing you want to have around are dry wood termites.

Actual termites or remains from long gone termites? How big is the thing? Does it fit in a garbage bag? Freezer? Termites are pretty big critters and in a discrete piece of furniture can probably be taken out thoroughly, but it really depends on what you have, both shelf-wise and termite-wise.

It is a pretty decent size hutch, 6ft tall, 4 wide. I cleaned it and painted it then a few days later the little wood stuff from termites on the floor...

return it.

Is it old or recently imported? What does the hole look like? What part of the world are you in? There are different termites in different parts of North America, although none of them are especially known for eating furniture...but there are many other wood eatign insects out there so it would be ideal to get an actual animal to identify.

Weather permitting, you can probably construct some sort of bag from multiple garbage bags and tape and fumigate the hutch.

You may be able to get locality specific advice from your local agricultural extension office.

I live in Costa Rica now, can a termite spray work?

Costa Rica has dry wood termites, and they eat anything made of wood (furniture or not).

They even eat living trees.

Borax dissolved in antifreeze will kill the termites.

Well shoot--antifreeze alone will kill termites, as will soapy water or a well-placed shoe.

I think I'd try an insect fogger, in a black bag, and leave it in the sun. Black cars are great for this.

I'm afraid your fresh paint might suffer.

The glycol in the antifreeze helps transport the borax deeper into the wood. Glycol also penetrates most paint finishes - except epoxy and polyurethanes.
The borax will remain in the wood as long as it remains dry and will kill future termites which try eating the wood.

When I lived in Miami I had a couple of pieces vault-fumigated, and I'm sure there's probably someplace in CR that could do this. It's not expensive if you aren't fussy about the timeframe and can let them wait till they have a vault full to do at once as opposed to making them do a whole run just for your piece.