I don't think there is a country that everyone would agree as the cheapest (and better) country.
There is a nice community-contributed index here: http://www.numbeo.com/cost-of-living/rankings_by_country.jsp
India is the cheapest country per se, but in the northern region, there are some cities that you can spend same, or even more than one would spend in Europe or the U.S.
As mentioned in the comment, it wouldn't matter $10k or $100k.
The link above also has information about housing, food, transport, etc. calculate it to match to your loving style.
The reason I said this can be different from person to person is that, Sri Lanka is also in the list's lowest cost, but almost everyone spends a lot that this minimum. Lives of these countries are very different from each other.
Also, some countries have dual pricing for foreigners and locals. The very same meal would cost twice in the same restaurant, higher ticket prices, minimum rent requirements, and there are several other things to consider.
I have been at Singapore, beating their high expenses, and I have lived in Sri Lanka, matching one would spend in Singapore. It's really up to you.
If you are actually planning to do this, Sri Lanka would be a good choice. Even my next door family is Canadian, lives a very normal local-ish life, and their cost should be about 600-1000 a month (we pay the same monthly rent and shop in same markets so it should be :) ).