Is there any way for the API interface to clearly indicate that Shopify stores or products have been

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Is there a clear field indicating whether it has been voluntarily shut down or taken down by the official? If not, how can I know?

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No official indicator is shown publicly.

indicator	Voluntary Shutdown	Shopify Takedown
Message: "Store unavailable"	Yes	Yes
WHOIS domain expired	Yes	NO/Yes
Abrupt access loss (partner view)	Yes	Yes
Confirmation from Shopify	No (Only if you're the owner)	No