Saw this in my textbook. The translation is "to preserve food from decay". I get it, but I am not clear about the ず after 腐らせる. Where is it coming from?
-zu is a negative particle. It is equivalent to the negative -nai. kusarasezu ni means "without letting [it, the food] rot".
ず is actually a 助動詞 to make a verb negative. It originates in classical Japanese. In earlier times, 知らず was written as 不知 (same as in classical Chinese) literally, not+know.
Frequently used is 残らず、知らず、せず（する）