This is a great question, and not a hypothetical one. In fact, there are places in the world that have essentially no IP protection. As always, it's hard to say what the "results" are, since these places didn't switch from a IP to non-IP environment, but it can be interesting to compare.
The first example is China[1]. Chinese consumers have been raised in an environment where everything can and will be pirated over and over. "Chinese consumers 'won’t pay a penny' for recorded music," claims the article. Yet, artists are still producing a steady stream of music. The article is, sadly, short on details about how musicians and music distributors actually make money. Perhaps it's via advertisement? In another article that I can't for the life of me find, it seems that the only Chinese musicians that make any money at all have massive star power and can command high ticket prices. So, the Chinese music market has turned in to a publicity machine to sell celebrity and the resulting high ticket prices.
The second example is "Nollywood", or the massive Nigerian film industry[2]. In this case, the film studios have about a week before pirates manage to distribute new films. The only way they can make nmoney is to produce, well, a new film each week. I posit that the films would be of higher quality if there was less piracy.
So, I think it's fair to say that there can be such a thing as too little IP protection.
1: http://www.economist.com/node/17627557
2: http://www.economist.com/node/17723124