I don’t know when mounting strobes the wrong way around inside softboxes became a thing. But, apparently it is. More mysterious than the “when”, though is the “why?”. The Shwop is a new product on Kickstarter that lets you do exactly this, though. Reverse mount a strobe inside a softbox.
They do list a few benefits of working this way on the campaign page, although I’m not entirely convinced. Putting me off even further is the fact that what essentially amounts to a fancy flash bracket costs more than the strobes it holds.