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There are a lot of questions here on what predatory journals are, and how to tell if a journal is one or not.

Are there known cases where a journal has "switched" camps, or where substantial evidence has been presented that they have? That is, has it ever occurred where:

• A journal developed a strong reputation for being predatory, recognized this, and engaged in a good-faith process of reform, eventually gaining at least a non-trivial amount of scientific credibility or impact?


• A journal with no history of predatory behavior suddenly started showing signs of becoming a predatory journal? For example, a publisher may have fallen on hard times, or been scooped by wealthier journals, and decided to lower their standards to such a level as to become predatory in order to survive.

For example, if someone has claimed, "The Podunk University Journal of Advanced Best Practices in Intermediate Spline Reticulation used to be a low-impact but serious journal, but after Podunk U was rocked by a cheating scandal in 2003 and there was a gradual movement away from Spline Reticulation toward Spline Retransmogrification from about 2005 to 2010 with a corresponding drop in the number of serious papers on Spline Reticulation being submitted, they started becoming a 'pay for play' publication and nowadays mostly publish incomprehensible screed written by rich patrons who want to increase their publication count.", that would count.

This question isn't really answerable because what's predatory and what isn't predatory isn't well-defined.

If you define "predatory" as being on Beall's list, then the answer is yes: MDPI was on Beall's list in 2014, and then removed in 2015 (there are a few other publishers that bounced back and forth on the list too, e.g. Hindawi). However if you believe that MDPI was not predatory to start with, or if you believe that MDPI is still predatory, then saying this publisher has switched from being predatory to reputable makes no sense.

The same goes for the other bullet point you mentioned (of a reputable journal becoming disreputable). In 2016, OMICS - a publisher generally held to be disreputable - acquired two Canadian publishers Andrew John Publishing and Pulsus Group, as well as their journals. You can see from the Wikipedia page that this "led to a decline in publishing standards". However if you read the quoted source, the objection is:

Rose Simpson, the former managing editor of the Canadian Journal of General Internal Medicine, said that after the OMICS deal was announced in January, she went on the company’s website and immediately noticed red flags as she started browsing through the journals.

“There were all kinds of typos, the grammar was wrong,” she said in an interview from Ottawa. “In medical journals, everything has to be accurate -- every comma, every word -- so that was my first suspicion.”

In other words, the decline in publishing standards is based on poor copyediting. Does poor copyediting make these OMICS-acquired journals predatory, given that poor copyediting can happen even in reputable journals? You'll have to come to your own conclusion. Rose Simpson clearly thinks so, but not every reasonable person will agree with her.

The Publisher Frontiers was - and, since there is no further development, still is - listed on Beall's List. Starting from scratch and with problems and therefore seen as predatory in the beginning by some researchers, Frontiers is now a reputable publisher with their journals listed in Scopus, Web of Science and the Journal Citation Report. The whole story is even included in Frontiers' Wikipedia article.

OMICS International, a “predatory” publisher of fake and low-quality research, has bought another Canadian science publisher — its third this year.

OMICS has acquired Intellectual Consortium of Drug Discovery & Technology Development Incorporation, of Saskatoon. Jeffrey Beall of the University of Colorado, who investigates the shadowy world of fake science publishing, discovered OMICS has expanded the group from three to 10 journal titles, all of them operating only online.

--Predatory publisher expands control of Canadian science journals

One of the world’s most well-known “predatory” publishers has bought two commercial Canadian publishers of about 16 medical specialty journals

--Alleged predatory publisher buys medical journals