One who has asked to keep receiving. A subscriber consented once and may withdraw at any time.
Latin subscribere (to write beneath, to sign one's name under a document), from sub (under) + scribere (to write); a subscriber has always been one who signed to keep receiving something, and could withdraw the signature.
One who has asked to keep receiving something, having signed on once and free to withdraw the signing at any time. Consent given, and never permanent for being given.