The company bought me unemployment benefits of 12 months, and I went to the Social Security Bureau to say that I couldn't get them because I didn't pay them. What happened?

You received unemployment benefits in June, July and August because your previous employer bought you unemployment insurance, and you were unemployed in the employment system of the Social Security Bureau. When you find your next job, the state pays unemployment benefits to protect your basic life, that is, unemployment benefits stop after you find a new job. If your current employer wants to supplement your previous social security, that is to say, it is obvious that the employer did not sign the labor contract and purchase social security in time when hiring you, and did not declare your employment status to the labor department.

If your company can make it up for you, of course it's best.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.