Kammarkollegiet is an agency that covers different tasks from the Swedish government, mainly activities that require qualified legal and economic expertise.
One of its tasks is to provide insurance for students at Swedish universities, including doctoral students who are not employed. Here you can find the agency’s guide to student insurance.
During time spent at the university, as well as during commuting time to and from school, you are covered by Personal Injury Insurance for Students. You are covered automatically and there are no special papers for you to sign.
Kammarkollegiet also offers insurance covering sick leave and parental leave or doctoral students with scholarships (called stipends on the Kammarkollegiet website). This insurance applies to doctoral students who don’t have equivalent insurance from another source. You can consult the terms of the insurance on the agency’s website, here. You can also ask the HR department or administrative staff at your institution about this insurance.