If something stabilizes, it becomes fixed or stops changing.

He suffered a second heart attack two days ago but his condition has now stabilized. 他两天前心脏病再次发作，不过现在病情已经稳定了。

If you stabilize something, you cause it to become fixed or to stop changing.

In China, the policy of one child per family was introduced to stabilize the country's population at 1.6 billion. 中国执行独生子女政策是为将其人口稳定在16亿。