Health coverage rarely comes automatically with the permit itself; it comes from the system the permit plugs you into, and countries wire this differently. In nations with social insurance systems, much of Europe and parts of Asia and Latin America, legal employment enrolls you more or less automatically: payroll contributions, deducted alongside those of your employer, buy you into public healthcare and often pension, unemployment and disability coverage too, with your registration handled during the onboarding paperwork. In other countries, employers must provide private health insurance as a visa condition, common in the Gulf, while a third group leaves health cover essentially to you, making private insurance a personal necessity. Several countries actually require proof of insurance before the visa is even issued.
Enrollment mechanics usually involve obtaining a social security or health system number early in your stay, one of those first-week bureaucratic errands worth prioritizing since medical care, and sometimes salary payment, waits on it. Ask your employer's HR precisely what is covered, when coverage starts, whether dependents are included, and whether waiting periods apply, because gaps between arrival and enrollment are where nasty surprises live; a short-term private policy bridges that window cheaply.
Also worth asking: whether your home country has a social security agreement with your host, which can protect pension contributions from being lost across borders. The national health or social insurance authority's website spells out the local rules definitively.