The central question is whether EU citizenship is a relationship between individuals and the EU, or whether it is simply an artefact of the treaties between the EU states.

If the former, then the action of a member state deciding to leave the EU could not remove EU citizenship from individuals, any more than one someone holding joint French and British citizenship could have their lawful French citizenship voided against their will by an action of Britain.

If the latter, then EU citizenship is not really a separate concept per se, but merely a term to describe an individual who has national citizenship of an EU state at a particular moment in time. Their individual rights exist through a layer of indirection: individuals derive their EU rights from their national citizenship only.

I believe the latter is closer to how it works in practice, however I can definitely see how such an interpretation could sit uncomfortably with the EU -- if there is no legal relationship between individual EU citizens and the EU, then one could start to doubt whether the EU itself is an entity per se, or if it is just a convenient term we use for the collective effects of the treaties between member states.