His employer may facilitate his saving preferences with some kind of program, but if not, it is quite easy for an individual to establish a savings plan with any number of financial institutions. If he becomes unemployed, he would draw upon the funds in his savings account at whatever rate he thought best. Notice that reliance upon individual initiative desocializes the risk of unemployment. No longer would one person's misfortune or laziness be a burden to everyone else. Also, notice that it works without the need for any government bureaucrats, further reducing the burden upon the taxpayers.
Insurance is the voluntary pooling of risk.
We have never had a market for unemployment insurance in the U.S. because state insurance regulators blocked it in the early years of this century because of the government's entry into the field during the New Deal. But there is no reason why there cannot be private unemployment insurance. You can already purchase insurance to cover your mortgage payments if you should lose your job. Unemployment insurance might be provided as a fringe benefit or might be purchased individually. By getting the government out of the picture, we would enable individuals to customize their preparations for the possibility of unemployment to their own perceived needs.