Louisa_xy

while selling to... = while the disigns of ...was sold to...
while 从句的主语the disigns of ...被省略了，因为从句的主语和
主句的主语一致。
while/when 引导的状语从句中主语和主句主语一致，状语从句即可简化为 while/when...+doing/done这样的副词短语
如，While I watch TV, I like to eat snacks.
= While watching TV, I like to eat snacks.
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sell to ...in record numbers和sell in record numbers to ...
sell的宾语直接放在sell后面，状语放在其后更好。

Louisa_xy

我想考的不是主动/被动，sell 用主动形式表达被动含义时（the designs of...被卖掉），是不及物动词，后面加well等副词。
sth. be sold to...而不能说 sth.sell to ...

Louisa_xy

while selling to... = while the designs of ...was sold to...
可以成立的。
while selling to = while being sold to...=while the designs of ...was sold to
while the designs of ...was sold to..和主句主语一致，主语省略变成while being sold to...，being 可以省略，就变成while selling to...