If the first nai is an auxiliary, ~naku wa nai ～なくはない means something "is indeed" somehow. If the first nai isn't an auxiliary, then it depends on what the phrase is saying. The exact grammar has been explained in the article about ~ku wa ～くは.
Usage
Phrases ending in ~ku wa nai ～くはない affirm something "is not" somehow.- kawaii
可愛い
[It] is cute. - kawaikunai
可愛くない
[It] is not cute. - kawaiku wa nai
可愛くはない
Cute, [it] is not.- Often implying it's something else. (see: contrastive wa は.)
Above, ~ku wa nai affirms it "is not" kawaii.
Then, with ~naku wa nai ～なくはない, it'll affirm it "is not" nai. But nai means "not." So it becomes it "is not not," nakunai なくない. Which means it "is."
- kawaii
可愛い
[It] is cute. - kawaikunai
可愛くない
[It] is not cute. - kawaikunakunai
可愛くなくない
[It] is not not cute.
[It] is cute. - kawaikunaku wa nai
可愛くなくはない
Not cute, [it] is not.
Cute, [it] is.
Yep, this is a confusing double negative.
To make matters more confusing, nai ない can be suffixed to a lot of conjugations. For example, in the potential:
- taberu
食べる
To eat. - taberareru
食べられる
Able to eat. (potential.)
[Something you] can eat.
Edible. - taberarenai
食べられない
Not able to eat. (negative potential.)
[Something you] can not eat.
Inedible. - taberarenaku wa nai
食べられなくはない
Not able to eat, [it] is not.
It's not [something you] can not eat.
It's not inedible.
Usually, the phrase above, taberarenaku wa nai 食べられなくはない, means it's something that you would rather not eat, but that it's not like you can't eat it. For example, if there's nothing else to eat, you'll have to eat it. So it's not like you can't. But, if possible, you'd rather not.
無くはない
When naku 無く is not an auxiliary attached to a verb or adjective, it means "nonexistent," which is the antonym of aru ある.The grammar of naku wa nai 無くはない remains the same, except this time we aren't negative a verb or adjective. Instead, we're negating something "not existing," or "not being in [our] possession," in other words, "[we] not having" something. For example:
- okane ga aru
お金がある
There is money.
[I] have money. - okane ga nai
お金が無い
Money is nonexistent.
[I] don't have money. - okane ga naku wa nai
お金が無くはない
Money, nonexistent is not.
Not having money, [I] don't.
Having money, [I] do.- i.e. it's not like I don't have money, I do.
An example with the null particle:
- kankei naku wa nai
関係なくはない
Relationship, nonexistent is not.- It's not like there is not a relationship.
- It's not like this has nothing to do with that.
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