Need help parsing "Everything I moved here to get away from"

I was just watching Homeland and the main character, Carrie, referred to her old life as "everything [she] moved here to get away from". I understood what she meant but had to pause the video to parse the sentence structure, to make sure it makes sense in my head. Something about it seems backwards, and yet I can’t think of a better way to phrase it.

I think it’s doubly confusing because there’s a final "verb-with-preposition" ("get away from") coupled with an inversion ("everything" moving from the final to the initial position.)

I think this is basically the same phrase structure as "what I came here to do." I’m wondering how to parse it. I think at the top level we have the nounish "what" qualified by the description "I came here to do" which is a subordinate clause that is missing its object. Is that a reasonable interpretation? Is there a name for this phenomenon?

Some more examples of what I feel is a similar structure:

• "You got what you came for."
• "That’s what I tried to tell you."
• "This is nothing I haven’t seen before".

After writing those out, I have another observation: it seems to work only with interrogative and indefinite pronouns?