While there are techniques to evaluate the “design, effectiveness, and impact of social protection programs on poverty reduction and income distribution” there is not a theory per se which guides this, rather a wide range of specific theories play a role.
More generally with regard to a concept of ‘Social Protection Theory’ there are again many different approaches – one useful starting point is The Three Worlds of Welfare Capitalism by Gøsta Esping-Andersen. Tracing the roots of social protection policies, and the underlying motives (which at times had theoretical underpinnings) also needs to be considered on a nation by nation basis – for example in Germany one can suggest this can be tied to the development of social insurance and other supports going back to Bismark in the 1880s, while in the UK one might suggest the Beveridge Report (William Beveridge: Social Insurance and Allied Services) published in November 1942