There is a difference between נשאר and נותר (remain): נשאר indicates that it remains intentionally, while נותרindicates that it remains of its own accord but not intentionally.

And from this, the difference furthermore stands in that נשאר was not joint with the whole, while נותר was joint with the whole.

Leviticus 10:12 says,וידבר משה אל אהרן ואל אלעזר ואל איתמר בניו הנותרים קחו את המנחה הנותרת מאשי יהוה ואכלוה מצות אצל המזבח כי קדש קדשים הוא(And Moses spoke to Aaron, and to Eleazar and to Ithamar, his sons that were left: 'Take the meal-offering that remains of the offerings of the LORD made by fire, and eat it without leaven beside the altar; for it is most holy). The wordהנותריםwas used for “that were left”and not the word הנשארים, since Eleazar and Ithamar remained alive of their own accord but not intentionally⁶⁹⁸.

footnotes: ⁶⁹⁸ Malbim, HaTorah v’HaMitzvah Shemini 41.