This is the 8912th most frequent Japanese word.
残さ
"残さ" is the stem form of the verb "残す," meaning "to leave behind" or "to save."
In this sentence, '残さ' is conjugated from the verb '残す' (to leave something), used here in the negative form, indicating not leaving any food.
最後まで食事を残さず食べました。
I ate the meal without leaving any behind.
Here, '残さない' derives from '残す' and is used in the negative form to express that no key was left.
彼は鍵を残さないで家を出てしまった。
He left the house without leaving the key behind.
'残さない' in this example suggests a precaution to avoid leaving personal belongings behind, derived from '残す'.