The city Göteborg had several parishes, in this case you are looking for Göteborgs Karl Johan parish.
If you are using Genline (or Ancestry.com) I think the death records for 1871 should be in the SCB records for the county (Göteborgs och Bohus county).
Probably in GID 100014.57 (probably starting at 100014.57.39400) according to the Genline web-site http://www.genline.com/databasen/walk3.php?x=14_100014
There are also household records, but if I recall correctly, it is difficult to find people in them.http://www.genline.com/databasen/walk3.php?x=14_896
// Bo Johansson