-ず and -ぬ are two alternatives to the negative form -ない / -ません. But I noticed that depending on the word, it's either -ず or -ぬ, although it seems like some words can take both suffixes. Some examples I have encountered:

-ず

知らず (lyric in song "タッチ" by Younha)
わからず (lyric in song "愛するもの" by Angela Aki/アンジェラ・アキ)
せず (song title: "油断せずに行こう")
なれず (lyric in song "未来へ" by Kiroro/キロロ)

-ぬ

気づかぬ (lyric in song "ありがとう..." by KOKIA)
届かぬ (song title: "届かぬ想い")
ならぬ (lyric in song "春雷" by YeLLOW Generation)

both -ず and -ぬ

とらず / とらぬ
できず / できぬ

So are there rules for choosing between -ず and -ぬ?