Also known as "bswap ax", and research shows that it does something surprising but consistent on almost all hardware: It zeros the register.

https://www.ragestorm.net/blogs/?p=141

https://gynvael.coldwind.pl/?id=268

However, this page, now gone, suggests that some CPUs (early 486s?) did something different: http://web.archive.org/web/20071231192014/http://www.df.lth....

Unfortunately I have not found any evidence nor reason to believe that this "inner swap" behaviour you mention exists in some CPU --- except perhaps some flawed emulators?