The point is the graph of data dependencies in an FP system doesn't necessarily look any different than in an OO one.

Closures and internal state of objects are basically the same thing.

I don't usually deal with stateful closures. In OO we often have file objects, and if you call Close() on said object, subsequent Read() invocations fail because the encapsulated state has changed. What's the closure analog for this?

You've never worked with a generator before? That's a stateful function. For throwing after a file handle is closed, something like -

  const read = (fileHandle) => {
     return () => {
       if io:isOpen(fileHandle) && io:hasNext(fileHandle) => {
          return io:readNext(fileHandle)
       } else if io:isOpen(fileHandle) {return undefined
       } else {throw "File is closed"}
     } 
  }(myFile)

  read()
  read()
  io:close(myFile)
  read() //throws