It's Gestalt

So how come you can see a letter out of this, 

 and this

 but not this?

And how come this one works,

when it doesn't look like it should?

It has nothing to do with color, or value, or contrast, or the distribution of the pattern on the fabric.

It has to do with the way your eye SEES and interprets what it sees. It's Gestalt. We perceive objects such as shapes, letters, pictures, etc., as being whole when they are not complete. When parts of a whole picture are missing, our perception fills in the visual gap. It's called the Law of  Closure.

Your brain interprets the shape first, and even if the edges are missing, it "connects the dots" on its own. Which is why the fourth letter is "readable" and the third one isn't. In the last example, your brain has enough information to complete the shape, to overcome that "lost edge" on the right, and "read" the letter as an "a."