They can do that especially on windows or mac but also linux.
They can just do frameset-alike targeting html tags on your local files and check for responses or errors (you can even attach debugger in JS!). Let's say you have profile picture on C:/favicon.ico can also do %appdata%/ms/ thumbnails db, ie cookies/history, profile picture on new windows, browser cache favicon.ico etc etc etc they can then screenshot or fetch it with the magic of turing complete Javascript and even hide the code under a base64 -> ??? -> base64 -> html script tags so you'd mistake as just another bloated URI (actually they're very dangerous!).
What's stopping them from doing so? It's free, just neckbeard and no funding required. We hacked android with a measly png file, we hacked windows with a INI text file, an entire server with a malformed GIF, ruby, command address injection on OS or on SQL.
The world is your cloyster.
If you're one of those "proof I don't believe you" people then I'll tell you that they can fingerprint your entire system font list with a simple JS.
Sometimes even a few bytes - bites!