Reproduction Steps:
1- Download attached project.
2- Build solution ResourceLoader.
3- Put built assembly(ResourceLoader.dll) into Assets folder.
4- Load project in Unity.
5- Create empty object.
6- Add "Loader" component to that object.
7- Save scene.
8- Enable embedded resources for WebGL export via "WebGL->Enable Embedded Resources".
9- Make sure "Enable Exceptions" is set to None or Explicitly Thrown in WebGL Player Settings.
10- Export WebGL project.
11- Load index.html.
12- Check browser's developer console output.

Expected Result: "text from resource" is printed to the console.
Observed Result: "stream null" is printed to the console.

Reproduced with: 5.6.0b6, 5.3.6f1

Note: Set "Enable Exceptions" to "Full" in WebGL Player Settings to achieve the expected result.