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Agent based simple exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk aversion factor, two agents are selected sequentially and randomly to exchange of wealth, which allows for their redistribution. In this contribution we analyze how the effect of a social protection policy, which favors agents of lower wealth during the exchange, influences stability and some important indicators of the system, like wealth distribution function, Gini index, and liquidity.  Besides, we compare two different exchange rules.  On the other hand, we study how periods of suspension of those policies give rise, in the short and long term, to changes in the system. In mostly all the scenarios, a stable state is attained, but with different relaxations times. We conclude that social protection policies can beneficially influence the system, increasing economic mobility and reducing inequality. Moreover, our results indicate that the withdrawal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Not only economic inequalities increase during a period without social protection, but they remain high for an even longer time and, in some extreme cases, inequality may be irreversible.