grammar - Meaning of volitional passive form

お姉ちゃんに何を言われようが、まる子はウキウキ気分なのであった。
What was said by her sister ???? but, Maruko felt cheerful.

I can't think of any way in which something which is passive can also be volitional. How do I understand this construction?

Answer

「何, どこ, だれ, いつ etc. + ～～(よ)うが」
「何, どこ, だれ, いつ etc. + ～～(よ)うと(も)」
「何, どこ, だれ, いつ etc. + ～～ても」

mean "No matter what, where, who, etc. ~~". For example:

何を言おうが / 何を言おうと(も) / 何を言っても
(No matter what ~~ say, ...)
どこに行こうが / どこに行こうと(も) / どこに行っても
(No matter where ~~ go, ...)
何があろうが / 何があろうと(も) / 何があっても
(No matter what happens, ...)
何を頼まれようが / 何を頼まれようと(も) / 何を頼まれても ← passive + よう
(No matter what ~~ is requested)

The auxiliary verb よう has other meanings than volitional. I think the よう here is #5 in デジタル大辞泉: 「仮定の意を表す。」(expresses a hypothetical/conditional meaning).

So your example:

お姉ちゃんに何を言われようが、まる子はウキウキ気分なのであった。

is like 「お姉ちゃんに何を言われようと(も)～」, 「お姉ちゃんに何を言われても～」, (Lit.) "No matter what Maruko was told by her sister, ~~" -> "No matter what her sister said to her, Maruko was feeling just so excited / exhilarated."