Not quite. Capitalists agreed to make temporary concessions, with the dissolution of the USSR there was no longer a rival system that offered good safety nets with fewer resources and under constant siege. Then, the capitalists removed them over time. See here:

For capitalists, welfare comes from taxation, which as paid from the social fund this includes coming from worker's wages. Welfare is merely like electricity for a capitalist, both necessary in that they maintain the conditions for commodity production, and as such both are minimized to the degree they can be, just like worker's wages.