You wouldn't believe someone will buy someone's cast-offs.

可以省略that的情况：
1.that引导一个成分完整的宾语从句：
eg：You wouldn't believe （that）someone will buy someone's cast-offs.
宾语从句：someone will buy someone's cast-offs.为一个成分完整的句子.
eg： I think （that）you are right.

2.that引导定语从句,且that在定语从句中作为宾语.
eg：The girl （that）I love is Daisy 我爱的女孩是黛西.
that I love 作为定语从句修饰前面的girl.且 that作为这个定语从句中love的宾语.
eg：the man （that）I admire most is Bill Gates.我最崇拜的人是比尔盖茨.

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