The Stockholm-based ambassadors are supported by an office (UD-KSS) at the Ministry for Foreign Affairs in Stockholm.
More about UD-KSS on ud.se

Swedish citizens in need of assistance should contact the
Swedish Consulate in Baku

Passport applicants are advised to renew their ordinary passport on the next visit to Sweden, or to contact the closest Swedish embassy.
List of all Swedish embassies

If you need an emergency passport, contact the Swedish Consulate:
Consulate of Sweden in Baku

Information about passports and national ID cards:
The police passport office