When this kind of nuance is used for the verb 知らない, why is the verb 知らない used even though it means "to know" and how do you translate it exactly...?
You could think of it as "complicitly knowing".
So, in the context of your example「知らない」it expresses something like:
So it could be translated this way...
- "If anything happens to you, don't come crying to me about it."
- "I can't be held responsible if anything were to happen."
Weblio has an entry for 知らない that shows the two usages:
If anything happens, I don't know (about anything)
This 知らない can be translated as:
"There is nothing that I can do"
"I won't be able to help you"
"I don't know about any way to help you"
"I won't care about you"