Kesi Sutta, what is an untamable person? "It is true, Kesi, that it's not proper for a Tathagata to take life.
  But if a tamable person doesn't submit either to a mild training or to
  a harsh training or to a mild &amp; harsh training, then the Tathagata
  doesn't regard him as being worth speaking to or admonishing. His
  knowledgeable fellows in the holy life don't regard him as being worth
  speaking to or admonishing. This is what it means to be totally
  destroyed in the Doctrine &amp; Discipline, when the Tathagata doesn't
  regard one as being worth speaking to or admonishing, and one's
  knowledgeable fellows in the holy life don't regard one as being worth
  speaking to or admonishing."


AN 4.111

Just so, is this subtle language? What then is an untamable person? Is it a being like an animal, who does not have access to Dhamma, or is it a being who has access to it, but disregards it out of hand, or something in between!?
Ven. Sujato translates it, "a person in training" (which makes sense in the context).

The word in question is purisadamma.

Piya Tan explains it here as follows:


  1.3.3.2 What is purisa? The usual translation for purisa is “person,” usually a “man.” And the usual
  word for “individual” is purisa,puggala or simply puggala, as if famously used in reference to “the pairs of
  persons, the 8 individuals” (purisa,yugāni aṭṭha,purisa.puggalā) in the recollection of the noble community (saṅghânussati).
  
  Here, purisa refers to a “person,” which loosely refers to a being with some capacity for thought and
  will (in the sense of personal action).
  
  The Buddha has tamed animal persons (tiracchāna,purisa), such as the naga-rajah Apalāla, Cūḷodara, Mahodara, Aggi,sikha, Dhūma,sikha, the naga-rajah Āravāla, and the elephant Dhana,pālaka.
  
  He has tamed human persons (manussa,purisa), such as the young nirgrantha Saccaka, the brahmin
  youth Ambaṭṭha, Pokkhara,sāti, Soṇa,daṇa, and Kūṭa,danta.
  
  He has tamed non-human persons (amanussa,purisa), such as the yakshas Āḷavaka, Sūci,loma and
  Khara,loma, and Sakra, the lord of the devas.
  
  1.3.3.3 What is damma? The word damma (Skt damya)
  is an adjective, the gerundive of dameti
  (causative: Skt dāmyati), “to bring into the house, to domesticate; to tame, convert; to be restrained;
  especially with reference to tamable animals; figuratively, to humans to be tamed or converted.” Technically, damma means “to be tamed, or should be tamed,” but the context here clearly refers to the
  capacity or readiness of a being or person for taming—hence, “tamable.”
  
  “Tamable persons” (purisa,damma), that is, those to be trained, according to the Sutta are of 4 kinds:
  (1) those who are trained with gentleness; [1.3.4.1]
  (2) those who are trained with harshness; [1.3.4.2]
  (3) those who are trained both ways (with gentleness and with harshness); [1.3.4.3] and
  (4) those who cannot be trained at all: the untamable. [1.3.5]