the hunger games - Why aren't more people breaking the law to survive by getting food from restricted areas?

Given the rampant hunger by many in Katniss' District 12, why aren't more citizens breaking the law and venturing into the restricted areas in search of food?

Answer

It's a combination of two factors:

1. 
   
   

   "Restricted" areas have dangerous predatory wildlife. To venture there even remotely consistently for a meaningful length of time, you absolutely must be armed with a real stand-off weapon, or you are lunch for something toothier.

   
   


2. 
   

   And of course, the Capitol would never allow people in the districts to be armed with real stand-off weapons (and not everyone is able to make their own). Peace-keepers sometimes tolerate someone who is able to make one for themselves and hide it in the forest - but few people are good enough to make their own weapons and making weapons for others is a Big Bad Thing Not To Do - that's how rebellions become viable.

   
   

Both of those points are explicitly explained in the very start of "Hunger Games", by Katniss (emphasis mine, the most critical sentence is italics+bold):

Electrified or not, the fence has been successful at keeping the flesh-eaters out of District 12. Inside the woods they roam freely, and there are added concerns like venomous snakes, rabid animals, and no real paths to follow. ...

Even though trespassing in the woods is illegal and poaching carries the severest of penalties, more people would risk it if they had weapons.

But most are not bold enough to venture out with just a knife. My bow is a rarity, crafted by my father along with a few others that I keep well hidden in the woods, carefully wrapped in waterproof covers. My father could have made good money selling them, but if the officials found out he would have been publicly executed for inciting a rebellion. Most of the Peacekeepers turn a blind eye to the few of us who hunt because they’re as hungry for fresh meat as anybody is. In fact, they’re among our best customers. But the idea that someone might be arming the Seam would never have been allowed.

In the fall, a few brave souls sneak into the woods to harvest apples. But always in sight of the Meadow. Always close enough to run back to the safety of District 12 if trouble arises.