Hi there, Snake65!
Thanks for reaching out to the Apple Support Communities! That is a great question you have about signing out of your iCloud on a broken device and I’m happy to help! To ensure your old device is totally removed from iCloud, I recommend you check out this article for iCloud: Remove your device from Find My iPhone. This will allow you to sign out of iCloud through the iCloud website and ensure your broken device is completely erased for you to sell.
If you no longer have the iOS device, Apple Watch, or Mac because you gave it away or sold it, you need to remotely erase it before you can remove it. With Apple Watch, you must have watchOS 3 or later installed to remove Apple Watch.
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Click All Devices, then select the device you want to erase. To erase:
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An iOS device or Apple Watch: Enter your Apple ID password or your family member’s Apple ID password. If you’re not using a trusted browser, answer your security questions or enter the verification code that is sent to your other devices. If you’re using your own computer and want to skip the verification step in the future, click Trust. If you’re using a friend’s computer, click Don’t Trust. If the device you’re erasing has iOS 8 or later, enter a phone number and message.
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A Mac: Enter your Apple ID password or your family member’s Apple ID password. If you’re not using a trusted browser, answer your security questions or enter the verification code that is sent to your other devices. If you’re using your own computer and want to skip the verification step in the future, click Trust. If you’re using a friend’s computer, click Don’t Trust. Enter a passcode to lock the Mac (you need to use the passcode to unlock it), then enter a message.
If the device is offline, the remote erase begins the next time it’s online. You receive an email when the device is erased.
Any credit or debit cards set up for Apple Pay on your device are removed from your device if you erase it, even if it’s offline. Apple Pay is also disabled for your device. For more information, see the Apple Support article Use Wallet on your iPhone or iPod touch.
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When the device is erased, click Remove from Account.
All your content is erased, and someone else can now activate the device.
You can also use a different iOS device to remove your device. For more information, open Find My iPhone, tap Help, then go to “Remove your device.” Or you can remove your devices from your account. For more information, see Manage your devices.
Even though you have the device and this specifically talks about no longer having possession of the device, these steps will also help when the device is not accessible and allow you to erase the device remotely.
Cheers!