When your Apple ID account is deleted, your account details and the data associated with your Apple ID are permanently deleted from Apple’s servers. You can't sign in to your account, and you won’t be able to access any data, content, or services that were associated with your Apple ID.
Apple warns you to make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.
For more info, see:
How to delete your Apple ID account - Apple Support
I don 't know of a nice way to say that you may now be stuck.