Third world countries can survive without external aid. Every single person in those countries may not survive without the additional food and clothing provided. The stop in the flow of aid however would not prevent the countries from surviving because most third world countries have a lot of farm communities which can produce food to survive.
If where they live does not have sufficient food or natural resources to trade with or if the land is damaged due to natural disaster or warfare then maybe they can not recover without the help of other countries. It is probably a situation that depends a lot on where they are.