if you have applied for a TIE card for a non EU and find that you need to temporarily leave the country, you would have to apply for an ‘authorisation to return’.
Translation taken from the site.
a) Be the holder of a residence or stay authorisation and have initiated the procedures for the renewal or extension of the authorisation that enables you to remain in Spain within the legal term.
b) Be a valid foreigner identity card holder and have submitted a request for a duplicate card due to theft, loss, destruction or disablement.
c) Prove that the trip responds to a situation of need and exceptional reasons concur and have the initial authorisation of residence or stay resolved favourably and have the issuance of the foreigner identity card in process. Translated from the Spanish text below:
SUPUESTOS
a) Ser titular de una autorización de residencia o estancia y haber iniciado los trámites de renovación o prórroga de la autorización que le habilita a permanecer en España dentro del plazo legal.
b) Ser titular de tarjeta de identidad de extranjero en vigor y haber presentado solicitud de duplicado de la tarjeta por robo, extravío, destrucción o inutilización.
c) Acreditar que el viaje responde a una situación de necesidad y concurren razones excepcionales y tener resuelta favorablemente la autorización inicial de residencia o estancia y tener en trámite la expedición de la tarjeta de identidad de extranjero.
Documents to provide to the National Police.
REQUIRED DOCUMENTATION
Note: in general, copies of the documents must be provided and the originals must be exhibited at the time of submitting the application.
Official model application form (EX-13) in duplicate, duly completed and signed by the foreigner.
Copy of the complete passport or registration document and valid travel document.
Copy of the application for renewal or extension of the authorization or of the foreigner identity card, or receipt accrediting its presentation.
In case c) (having granted initial residence or stay authorization and having a foreign identity card pending): documentation proving that the trip responds to a situation of need and exceptional circumstances concur.
Important note: when documents from other countries are submitted, they must be translated into Spanish or the co-official language of the territory where the application is submitted.