Why don't dry bread crumbs spoil, when bread does?
Bacteria need a friendly environment to live. They can't survive without mosture. Mold tolerates more, but it needs moisture for life too. 

Bread is too dry a food, so it doesn't catch bacteria. This is why it can be stored outside the fridge. But if you live in a moderately humid climate, it can still be moist enough for mold to grow, especially if stored in a non-breathing package (plastic bag). Drying the bread to the point where this won't happen is possible, but it gets quite hard then. Examples for such dry bread are zwieback or finnish crispbread. 

Store bought breadcrumbs are dried to the point where they can't catch mold. This is why they can be stored for so long. If you make your own in the food processor, they will be similar to bread. Probably a bit better, because the bigger surface will let them dry quicker than bread. But if you want to be sure they will last, dry them. You can use a dehydrator or put them in the oven at the lowest temperature (usually.50 deg C) and hold them there for 4 - 5 hours.