How does a Google iOS app save and restore active accounts across app deletion?
Apple advises developers to store app login credentials in the encrypted iOS Keychain. When you delete an app from your phone it doesn't delete the related records from the Keychain.


  Keychains are secure storage containers, which means
  that when the keychain is locked, no one can access its protected
  contents. In OS X, users can unlock a keychain—thus providing trusted
  applications access to the contents—by entering a single master
  password. In iOS, each application always has access to its own
  keychain items; the user is never asked to unlock the keychain.
  Whereas in OS X any application can access any keychain item provided
  the user gives permission, in iOS an application can access only its
  own keychain items.


https://developer.apple.com/library/ios/documentation/Security/Conceptual/keychainServConcepts/01introduction/introduction.html