While browsing StackOverflow I accidentally stumbled upon this question.
The issue seemed like a simple but interesting one, and since google had no answers I thought it would be fun to give it a shot. The first iteration of my solution involved reading in strings of indefinite length, but it quickly turned into a overly-complex state machine so I stepped back and rewrote it with one-character-at-a-time input. You can find on github, under JSONCharInputReader.

JSONCharInputReader was designed to read in a JSON array, not object.
In other words, this will work:

[1, 3, 4, {"var": "val"}, ["array_item", "array_item"], ...

but the following will not:

{"key": ["array", 1, 2], "key2": "value", ...

To parse a JSON stream, create a JSONCharInputReader object and pass in your own implementation of the JSONChunkProcessor interface. JSONChunkProcessor defines one function:

interface JSONChunkProcessor {
    public function process($jsonChunk);
}

Clients implementing this can expect $jsonChunk to be valid JSON (as long as the JSON data being read in is valid itself). If the above array was to be read in, the decoded $jsonChunks passed to the processor would be as follows:

// Decoding 1
int(1)

// Decoding  3
int(3)

// Decoding  4
int(4)

// Decoding  {"var": "val"}
object(stdClass)#3 (1) {
  ["var"]=>
  string(3) "val"
}

// Decoding  ["array_item", "array_item"]
array(2) {
  [0]=>
  string(10) "array_item"
  [1]=>
  string(10) "array_item"
}

See example.php for a sample implementation of the reader, which can read JSON from the terminal by executing it with:

cat | php example.php

One notable limitation is that the $jsonChunks passed to JSONChunkProcessor will be first-dimension level elements of the incoming JSON array data stream. In other words, large objects or arrays will only be processed once the reader receives all of their data.