Everyone working in Sweden is covered by unemployment insurance, but if you are not a member of a voluntary unemployment fund (A-kassa), the insurance payout is very low (SEK 365 per day in 2017). To be eligible for unemployment insurance, you must have been working for at least 50% of fulltime for at least 6 months during the last 12 months. Employees on fixed term contracts who intend to stay in Sweden are strongly advised to become members of a voluntary unemployment insurance fund (A-kassa), since members receive payments based on their salary; this is called income-based benefit. If you are not a member of an A-kassa you can still be eligible for unemployment insurance but at the basic rate. More information about unemployment insurance in general is found at Arbetsförmedlingen.
See also Akademikernas A-kassa, an unemployment insurance fund for academics.