Just wondering this: when placing a new puzzle piece, it must extend at least one previously established line. Is it permissible for the new piece to, say, simply hit a wall? i.e. can it dead-end itself?

For example, is it permissible to place two | pieces on top of the starting piece (this will lead it to a wall), or is it only permissible to play a corner or crossroad piece after the first one?

In other words, is it possible to dead-end the entire conspiracy?

I'm not clear on what exactly you're asking, just because of the phrasing of the last couple of paragraphs. However, it's certainly permissable to place a piece of the conspiracy that connects back to the central piece, but rams it's only line(s) straight into the edge of the puzzle, or onto the blank side of another piece. The only rule with placement it that it has to connect one edge of the piece that has a line to one edge of a piece alread in play with a line. It's actually a fairly effective strategy to make sure the conspiracy doesn't always connect to everything--for instance, if you've a character with a lot of Corp favors, you certainly want it to connect with that, but if you have no Society favors and one of the others has a half-dozen, it's best to run the line going that direction into a wall before it can get there. Same if your guilty hunch just got killed--why bother letting someone else's guilty hunch pay off an extra 5 VP?

As for is it possible to keep the conspiracy from connecting with anything, it's certainly possible within the rules, but it would take a concerted effort by multiple players to do so. The conspiracy is too vast and complex for a single person to completely nerf it.

YES is the answer to your question.

As bcwMD says as long as it is within the rules that your last placed piece have a link into the middle piece of the conspiracy you are allowed to plant pieces that goes into walls and dead end them as you call it.

@bcwMD

Well it actually is in some way possible for one person to ram the Conspiracy, at least I was able to do it effectivly with Floyd in the last game I played him. Since he doesn't have anything that gives him bonus worth the favors in the same amount as the others I derailed every entrance to favors as soon as I was able to. But yeah you have to find the strategy to it against the players you play, and how much you think they will be able to place. But yeah it is hard and not always possible, cause luck of the draw also comes into the equation.