In Switzerland occupational disability insurance is usually for the first 2 years. After (usually) 2 years, it is the invalidity insurance with the first and 2nd pillars.
So everybody who is an employee is protected after two years of waiting period. Before that, not everybody is fully protected. The minimum requirement of the law is that in case of disability, the employer has to continue to pay the salary for a few weeks. How many weeks that is depends on your seniority in the company and of each canton’s scale. The number of weeks is reset to zero every year.
Many employers, even though they are not required to, insure their employees with an occupational disability insurance that will pay 80% of the salary for up to 2 years, connecting to the point where the first and 2nd pillar would take over. This frees them from having to continue to pay the salary. If your employer does not do this, you can also take an individual insurance scheme that does the same.
And if the first and 2nd pillar are not enough, you can also take an invalidity insurance in addition to them, which again usually starts after a two year waiting period.
Finally, what I said above does not apply to accidents: as far as I know all employees in Switzerland must be insured against accidents including the salary and without waiting for 2 years. Above a number of hours of work per week, this also includes being insured outside of work. Some employers offer against a monthly premium a complementary accident insurance but this can also be taken privately.