Based on what I saw traveling through South America for 5 months, $500 would be a stretch in Chile, Argentina or Brazil. A hostel or a really cheap apartment would probably be 2/3rds of that alone... especially as a white dude. You might be able to swing it in a place like rural Bolivia or an (for lack of a better work) economically depressed country in Central America (Panama, Guatemala), but I wouldn't really want to try. Think about it... your budget is $16/day. You'd basically be eating empanadas or similar for every meal, you'd have no travel budget, you'd be stuck living in either a really, really crappy apartment with 10 roommates or a hostel dorm... and even then it would be close. Honestly, a much more reasonable budget, where you would actually be able to enjoy your time and not stress about budget, safety and turning down a bunch of awesome experiences (soccer matches, trips to national parks, wine tasting...) is probably 2k/mo.
I speak Portuguese, which allows you to use websites like easyquarto to rent rooms at market value. R$1,000 is a typical monthly wage in most of the interesting parts of Brazil ($500US), and cost of living in Brazil has outpaced Chile and Argentina in recent years, although I'm not arguing I'm exempting Rio & BA since the cost of living is somewhat inflated. I've been to every part of Brazil on that budget (Outside of holidays), including airfare (Once you learn the pricing system), Even the super expensive island of Fernando de Noronha. We all cooked our own meals, with enough left over to splurge 2-3 times per week. In most places, travelers pay a steep premium for inexperience.
It is HIGHLY variable. A few years ago, Brazil was dirt cheap. Now, U$ 500 on Argentina would go a LONG way and will definitely get you there (if you avoid the "official" exchange rate) but Brazil is really expensive now and doesn't sound doable on U$ 500.
