Backshift in the Past (aorist → pluperfect, future → θα + imperfect)
The present is not the only reported tense that can shift. A reported AORIST may slide to the PLUPERFECT (Module 10): «Είπε ότι έφυγε» (kept) or «Είπε ότι είχε φύγει» (“he had left” - the pluperfect marks it complete before the moment of speaking). A reported FUTURE (θα + perfective) may shift to θα + IMPERFECT: «Είπε ότι θα έρθει» (kept) or «Είπε ότι θα ερχόταν» (“he would come”) - θα stays, the verb moves to the imperfect (έρθει → ερχόταν), exactly the θα + imperfect shape of the present-unreal “would”. The whole system is one tidy back-step: present → imperfect, aorist → pluperfect, future (θα + perfective) → θα + imperfect. Every shifted form is a tense you ALREADY own (imperfect Module 6, pluperfect and θα+imperfect Module 10), and every shift stays OPTIONAL - retaining the original tense is always available and often more natural in speech.
The rule
The present is not the only reported tense that can shift. A reported aorist may slide to the pluperfect (see The Pluperfect): Είπε ότι έφυγε (kept) or Είπε ότι είχε φύγει (“he had left” - complete before the moment of speaking). A reported future (θα + perfective) may shift to θα + imperfect: Είπε ότι θα έρθει (kept) or Είπε ότι θα ερχόταν (“he would come”) - θα stays, the verb moves to the imperfect (έρθει → ερχόταν), the same shape as the present-unreal “would”. The whole system is one tidy back-step: present → imperfect, aorist → pluperfect, future (θα+perfective) → θα+imperfect. Every shifted form is a tense you already own, and every shift stays optional - retaining the original tense is always available and often more natural in speech.