I would add that this isn’t just speculation, it has historical precedent. The US created a powerful welfare state under FDR and it was slowly destroyed in exactly the way that you described. It’s also important to note that it was racism that provided the owning class with the narrative they needed to convince the working class to support the erosion of their own welfare. The creation of the welfare state began with the compromise that the benefits would not extend to non-white Americans. When the civil rights movement successfully forced the issue and demanded that the benefits be universalized the owning class was able to ride the wave of the racist backlash all the way to a near-total rollback of the welfare state.

Ensuring that welfare for the people lasts requires that we directly and conclusively address the underlying causes of the inequality it is meant to alleviate. We must recognize that private ownership of the means of production is the direct cause of this inequality and will always reproduce it if it is not eliminated. And finally we must also address the social causes of inequality - racism, bigotry, xenophobia, sexism, etc. - so that they cannot be used as justification for the reconstruction of a system of inequality. Alongside an economic and political revolution we also need a cultural revolution.