subsidiary verb; auxiliary verb
A grammatical term for verbs that attach to the te-form of another verb to add grammatical meaning such as aspect, direction, or benefactive nuance. Common examples include いる, ある, いく, くる, しまう, おく, みる, くれる, あげる, もらう.
The いる in 〜ている is a subsidiary verb.
Subsidiary verbs need to be taught separately from main verbs.
補助動詞 are ordinary verbs like いる or おく that lose their literal meaning when following a te-form, whereas 助動詞 is a distinct morphological class of inflecting words attached directly to stems.
Compound of 補助 (hojo, 'assistance, support') and 動詞 (dōshi, 'verb'). The term is a modern linguistic coinage for describing Japanese grammar.