Judge Brack's last line (actually the last line of the whole play) aren't actually directed to Hedda, but to Tesman who has just shouted out that Hedda has shot herself. His remark, "Good God - people don't do such things", is almost a comic line, because people obviously DO do such things: Hedda has just done it.
It's a characteristically ironic, bitter finish to a play in which Ibsen has explored the meaning of appearances and what lies underneath them (and of course, this final line is only one of several moments where Judge Brack appears absurdly ill-equipped to read the situation). It also highlights the distance between Hedda and the society she lives in: her suicide, like her feelings, are so alien to the society in which she exists that they might as well not exist: indeed, Brack thinks they don't!
Hedda Gabler's biggest fear is people perceiving her as doing "worldy" things. Her wants and desires live only through listening to other people's drama and through hurting people emotionally in ways that cannot be traced or labelled as "evil". (The "hat" incident with her step-aunt.)
Ironic that Brack would say in the last line "People don't do such things." As far as she was concerned, at least she is not alive to see the ruin "killing herself" will cause to her reputation. Absurd to the audience that she would see this as her only option.
This combined with robertwilliams answer pretty much covers it