I am not a lawyer. The following is not legal advice. I strongly suggest you talk to a lawyer to seek legal counsel on your inquiry.
Having or not having DRM does not affect the original author's copyright. The author retains all legal rights and responsibilities as previously.
DRM does, however, give the author more legal teeth via the DMCA, which covers the circumvention of copyright protection measures, like DRM.
While someone who gets ahold of your DRM-free ebook can publish it for free elsewhere, they would be in violation of your rights, and you will have the right to issue a DMCA takedown against the site, and/or seek redress via a lawsuit.
Having DRM applied to your book doesn't exactly protect you from having someone strip the DRM off of the ebook and then going and publishing it anyways. They can actually publish the DRM'd copy as well and just leave the task of removing the DRM an exercise for the downloader.
For you, the author, DRM doesn't factor into your rights. It provides a mild hinderance to the would-be thieves and to a greater extent, a good deal of annoyance to your would-be fans and readers. DRM presents significant hurdles to your fans and customers from being able to read a document easily between devices or being able to retain the text past the life of the company that is handling licensing, the device that it is associated with, and so forth.
Note, publishing a text without DRM does not imply that you are making it public domain, just as publishing a xerox'able/scannable book does not mean it is in the public domain. DRM is a tool to hinder copying and is of variable effectiveness(some would say of little value except to the companies that license out DRM technologies).
Some publishing channels require DRM, others require there to be no DRM on your submitted titles. Some publishing houses will enforce DRM whether you want them to or not.