Just to think through this a little bit further. There is a proportion of "free-riders" in every given population, even those without a safety net. Some free-riders will exploit their own children, the government, their family's status, their spouse, or whatever or whoever is at hand. Some people decide they would rather be homeless than exploit anyone. In short, let us acknowledge that free riding is a thing that happens, and that it is usually morally reprehensible.

Which will lead to a more stable society: social safety net, or no social safety net?

In my experience and observation, societies that have protections from poverty seem to be far more stable as compared to societies that do not have them.