2

The full sentence is:

会社が業績不振で給料が30%カットされるなんて、そんなばかなことがあるものか.

Does it mean "such a stupid thing" or "not a stupid thing at all"?

4

「会社{かいしゃ}が業績不振{ぎょうせきふしん}で給料{きゅうりょう}が30%カットされるなんて、そんなばかなことがあるものか。」

Does it mean "such a stupid thing" or "not a stupid thing at all"?

The former - "such a stupid thing".

「あるものか」 means "there should never be (such a stupid thing)". In other words, 「あるものか」 is a negative expression that is synonymous to 「あるはずがない」、「あってはならない」, etc.

"There should never be such a stupid thing as getting 30% of our salaries cut down because of the poor business performance of our company."

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