ず＝ない 飲まず＝飲まない 食べず＝食べない 読まず＝読まない 行かず＝行かない 買わず＝買わない.... ect "飲まず食わず" is a phrase that we always use when we want to say "without drinking and eating". I think the sentence's translate is "Without eating and drinking, he barely made it back." You always ask very good questions! Those are good also for me to think about teaching Japanese. I hope you can understand my English though :)

Actually it's not -azu, you use the same stem form as for -nai and replace -nai with -zu: http://www.guidetojapanese.org/learn/grammar/negativeverbs2

飲まずで = without drinking 食わずで = without eating This is how you construct the "without ~ing" form in Japanese.

ず in 飲まず/食わず is the ren'yo kei form of the negative auxiliary "ぬ", another (a bit literary/archaic) form of ない.