To directly answer your question, you can see some research on damaged QR codes here: http://datagenetics.com/blog/november12013/
A barcode is nothing more than a specialized font designed so that a computer can read reliably. It's much easier for a computer to recognize and read a pattern of stripes than it is for it to read Courier or Arial. And just like the Latin alphabet symbols you're looking at right now, the symbols have to be readable to the machine. Just as we all agree that the letter 'O' is represented to humans by an oval shape, barcodes follow standards that describe the meanings of the stripes and dots.
However, the text that is printed by the barcode is not nearly as standardized. Some barcodes, like the familiar UPC and EAN barcodes, are strictly numbers that identify a product, and these do follow a standard. But others, like QR-codes, allow free-form text. A valid QR-code may contain a URL with a web link, or a vCard with contact information, or just some random words like "Have a nice day."
So there are as many different kinds of barcodes as there are kinds of text to input. If you want to prevent online theft, treat pictures of barcodes the same way you would treat a picture of your credit card. Do not include photos of personal documents showing these numbers or barcodes. This includes event tickets, gift cards, driver's licenses, and airplane tickets. Otherwise, an online thief may make a copy and steal the value from you.
To more specifically answer your question using this information, imagine a linear barcode with left half obscured. This is the equivalent of obscuring the first half of a sentence or word printed on the page. The right half remains legible, although it may not contain enough information to fully convey the message.
Now picture a 2D barcode, such as a QR-code. Many 2D symbologies are designed to include redundancy permitting accurate reading of the barcode, even when parts of the barcode are obscured or damaged. This is needed because damage to barcodes is very common in normal handling. So when a QR-code is generated, you can specify a level from 1-4 of redundancy you need the code to embed. They use a Reed-Solomon algorithm to add more error recovery symbols. More redundancy allows for a greater portion of the barcode to be damaged while still maintaining readability.