It doesn't speak for retail in general, but the article has a nice case study of grocery sector. Since 2015 7 PE backed grocery chains have filed for bankruptcy, no non-PE chains have filed. These companies were healthy before being taken over by PE.https://twitter.com/Molson_Hart/status/1119348827960553472 …
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That said, I don't think it should be illegal. There are certain complicated financial tricks that they use that potentially could use some regulation, i.e. having the LBO'd company make a loan to the company that is more senior than employee pay or vendor A/P are.
I don't know a ton about the space, but it's quite possible that, in the absence of competition from Walmart, that these chains would have been fine. The problem seems not to be private equity or debt alone, but debt paired with an unanticipated competitive threat.