First, I would probably start these sentences using had instead of was, or maybe use disappeared on its own:
He had disappeared so that...
He had disappeared such that...
He disappeared so that...
Collins mentions that the phrase so that is used to "introduce a clause of purpose".
You should wash your hands so that you don't catch a cold.
I left the door unlocked so that John could let himself in.
So, if you can think of a reason someone would disappear, you can use so that to introduce that reason:
Ed had two arrest warrants. When he heard the police at the door, he disappeared so that he would not be arrested.
It's worth pointing out – we can omit the that and these sentences would still be grammatically correct:
You should wash your hands so you don't catch a cold.
I left the door unlocked so John could let himself in.
He disappeared so he would not be arrested.
Collins also mentions that such that can indicate purpose or result. I would say that, when indicating a purpose or reason, so that generally sounds more natural than such that:
You should wash your hands such that you don't catch a cold.
I left the door unlocked such that John could let himself in.
He disappeared such that he would not be arrested.
For those three sentences, I prefer the sentences that use so or so that (although I'm not sure I could go so far as to say such that would be incorrect or ungrammatical).
However, such that can be used to express the result of the disappearance:
The hobbit put on the ring. The moment he did, he disappeared such that we could not see him.
Ed had disappeared such that the police could not arrest him.
As an aside, in the first sentence, "disappear" has a more literal meaning.