How is it possible that a company can copyright a phrase or slogan?

It can, according to the law, if is not taken, you can take it, it has to be directly related with the product or service you are offering, and obviously, pay a fee for the rights of the phrase

What if I thought of a unique phrase or slogan, ie.. can’t be found on google, but I didn’t have a product or service to attach it to. Would it still be possible to copyright said phrase/slogan and a few variants? If so how much could it cost and where/how would you do it?

Thanks for your previous answer!

You’re probably thinking of registered trademarks instead of copyright. Copyright law is applied to a work that someone creates—for instance a work of art—and it is, by default, copyright by them the moment that it is created. In this way if I draw a picture, write a musical composition, design a website, then the rights to that work belong to me, instantly and completely—with the exception of fair use exclusions—without any charge. (There is a way to have copyrights officially registered with the U.S. Copyright office, but generally speaking, people use the copyright symbol © regardless of a whether a work is registered or not).

Trademarks, by contrast, refer to names, slogans, phrases, designs, &c. for a product, specifically. Trademark can refer to common law trademarks, which work similarly to copyright law above (i.e., you don’t have to do anything, it’s yours by default), however these are difficult to uphold in legal proceedings. What it takes to have a trademark registered (the crux of your question) depends on jurisdiction you want it registered in, bearing in mind that your trademark will not be upheld in jurisdictions that you do not register it in (i.e., if I register a trademark with the U.S. Patent and Trademark Office, it likely will not be held up in foreign countries).

Additionally, and I am no expert on the subject, so take my word with a grain of salt, I think the U.S. Patent and Trademark Office is probably unlikely to register trademarks that don’t actually belong to a particular product. However, all the information you need to apply is on their website

You can learn more about trademarks, copyrights, and even patents from Wikipedia.

Thanks for the information and interesting links lapilofu! I will certainly look into them.