When losing to the USA on Wednesday, Britain had to defeat the Netherlands and perhaps Kazakhstan as well. However, Sunday's match will no longer have any significance after Andy Murray and Joe Salisbury once again lost a nail-biting doubles rubber.
The Dutch, who have a modest group of orange-clad fans, and the Americans, who each won two of their first two games, are the ones who can enjoy their advancement to the last-eight shootout in Malaga in November.
Dan Evans' 6-4 6-4 victory over Tallon Griekspoor gave Britain the perfect start after they were pushed out by the US extremely late on Wednesday night.
However, Cameron Norrie put on a bad performance to lose to Botic Van De Zandschulp 6-4 6-2, while Murray and Salisbury lost to Wesley Koolhof and Matwe Middelkoop 7-6 (0) 6-7 (6) 6-3 despite the best efforts of the Emirates Stadium audience to cheer on their home hero in his 50th Davis Cup match.
Murray and Salisbury got off to a terrific start by breaking the Middelkoop serve in the first game. Murray was once again chosen over Neal Skupski, who reached the men's doubles final with Koolhof at the US Open last week.
Britain saved a match point in the second tie-break and then won the first set point with the help of a supportive net chord.
The players, team, and fans rejoiced, but they still needed to win the final. Salisbury missed opportunities at 3-3 and dropped serve in the following game, leaving Koolhof to serve out the victory.
They will only be able to host a group stage for the following four years if they are among the top 16, which is likely to require winning a play-off early in 2023 because they can't possibly hope to receive another wild card.
The eighth-ranked player in the world has had trouble finding his game on the very sluggish Glasgow court and was outplayed throughout by Van De Zandschulp, who served 13 aces.