Has a journal ever switched between being a predatory journal and a reputable one?
This question isn't really answerable because what's predatory and what isn't predatory isn't well-defined.
If you define &quot;predatory&quot; 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 &quot;led to a decline in publishing standards&quot;. 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.
Edit: to further illustrate how much of a grey area there is in what's predatory and what isn't, consider a journal that doesn't perform peer review. Say this in a vacuum and most people will immediately assume the journal is predatory. If this is your definition, then there has indeed been a predatory journal that &quot;reformed&quot; and started implementing peer review: Medical Hypotheses.
The problem is, as you can see from the &quot;Peer review debate&quot; section of the Wikipedia article, this journal was started by a reputable academic (David Horrobin) and published by a reputable publisher (Elsevier). David Horrobin's stated reason for starting the journal is that peer reviewers tend to dislike ideas outside the scientific mainstream, which makes it hard to publish new ideas. His solution was to not perform peer review, and to worry less about whether the paper is true but whether the paper is interesting. Ironically, when put this way, there are people who agree with this sentiment too.
The upshot of this policy is that in 2009, Medical Hypotheses published two papers arguing that there's no proof that HIV causes AIDS. There was a backlash, the media got involved, Elsevier investigated and subsequently demanded the journal implement some level of peer review. The then editor-in-chief Bruce Charlton refused and was subsequently sacked. A couple of years later, 198 academics published an article in another journal defending Bruce Charlton and Medical Hypotheses' original peer review model.
Is Medical Hypotheses predatory? It didn't perform peer review and published pseudoscientific papers! Is Elsevier predatory? It fired an editor that didn't do what it wanted! Again, you'll have to come to your own conclusions. There's no clear answer.