i've recently bought a japanese scroll, for decoration, with a famous quote from " the last samurai": 吐く息一つにも生命が宿り . but i think this is incorrect: in the film this was part of a speech, and there was another phrase after, so of course it finish in "り". but if i'm gonna write this as a single phrase shouldn't i end it in "る"? so it should be:吐く息一つにも生命が宿る . am i correct?
A phrase ending in
-i (連用形) is its own way of expression, not necessarily wrong. Of course, whether it is apropos to use it in a certain situation is another question. Yes, it is "incomplete" as a sentence, but may not be "incomplete" in the way you think.
If you put it in equivalent English, it'd be like "life dwells in (each) a breath you breathe out, and", which would be felt quite truncated. But grammar-wise, it is merely another form in the verb's paradigm in Japanese, as if the difference between "I walk" and "I walked". Taking another example, A novel Brightness Falls from the Air by James Tiptree Jr. has a translated title 輝くもの天より堕ち, which is, by meaning, "brightness falls from the heavens, and", but grammatically comparable to "brightness's having fallen from the heavens" or "when brightness falls from the heavens". These English phrases are not "complete sentences" either, but are self-contained enough to be a title by themselves. It might sound like a brain twist because a piece of grammar, whose form is parallel to those English while carrying the Japanese meaning, is unavailable in English, but it is a basic device in Japanese.
If this is a partial quote from a longer sentence, you should not try to alter it, anyway.
In addition, ending a sentence with an i-form (stem) or a te-form is not necessarily a mistake. Making a "partial" sentence and not saying everything is a not-so-uncommon technique in poetry/lyrics, and doing so can leave room for the imagination. For example, one could name a song as 聖なる夜に雪は降り instead of 聖なる夜に雪は降る; this is not very common, but the former can look more dramatic.
Pre-masu form (stem form) can be used either to connect phrases (continuous) or to end a phrase/sentence (conclusive). While the latter usage is not found so often in contemporary Japanese, in phrases such as proverbs, holdouts from a more classical era have remained in the language. Changing the end to 宿る would not accurately reflect the origins and nuance of the phrase.
Looking up proverbs, you can find many that end with あり and other pre-masu forms.
終止形 (conclusive) and 連用形 (continuous) verbs are effectively the same, it is simply their usage that differentiates them.
'To know life in every breath.
Every cup of tea. Every life we take.
That is the way of the warrior.'