If a publisher owns the rights to their content and they go out of business how can you find out who owns it? Does the content they created and published become public domain? Who would own the copyright if the author IS the publisher?
The publisher does not own the copyright unless they create the work--the author does. In traditional publishing, the author typically gives a world-wide exclusive license to use the copyright to the publisher, though many small and mid-sized presses will only ask for rights to the areas or languages they distribute in. If the publisher goes out of business or the work goes out of print, the rights generally revert to the author. If the rights do not revert, they may get sold to creditors or other interested parties to help settle the publisher's debts. If the publisher goes under in a huge mess, it's possible that the manuscript will become an "orphan work"--which basically means that nobody is really sure who owns the copyright.
The short answer is it might, but only under special circumstances if the status of the new owner automatically puts it there.
It is relatively simple to verify how that could be the case, by interpreting the first sentence in Wikipedia:
Works in the public domain are those whose intellectual property rights have expired, have been forfeited, or are inapplicable.
which in itself is taken from Graber & Nenova¹
- The expiration of a work depends most often nowadays on a period of many years after the time of death of an author².
- Forfeiting is an active process by the copyright owner.
- Inapplicability is based on the type of content and its new owner, and that normally does not change with the status of the ownership.
Inapplicability could apply e.g. in the USA if the government hands out the writing of something like a building code to a commercial firm XYZ, and XYZ goes out of business at the code is finished, but the rights not transferred yet (government paying late?). Depending on the governments and other creditors status, this could result in the code transferring to the government and the code being in the public domain as such things if produced by the government normally are³.
This is comparable to a piece of private land automatically becoming publicly accessible because its right were left to some entity that has dedicated all of its properties in a certain area to be publicly accessible.
¹ Intellectual property and Traditional Cultural Expressions in a Digital Environment
² It is actually way more complex, but this seems the most common
³ And even in this hypothetical and convoluted case a government would not want this to be an official publication, although it might be in the public domain. You could also see this as some sort of auto-forfeiting by the new owner