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Stink bugs are nontoxic to cats, however some cats will develop mild digestive upset such as vomiting and or diarrhea. depending on the cat this can happen almost immediately or several hours later.Should this happen it normally resolves itself rather quickly.
Cats like to play with and often eat bugs so if you happen to see this it is recommend to remove the bug before it can be ingested.
I hope this has answered your question, please reply back if you have additional questions or concerns