The 2019 runners-up finish bottom of Group B after failing to win all six matches they played across two ties.
Elias and Mikeal Ymer secured the win for the Swedes over the Canadians on day one of the event.
The Canadian will look to lead his team one step further after reaching the final in Madrid back in 2019.
Muguruza caps off what she describes as her 'best year' on the Tour by becoming the first Spanish woman to win the season-ending title.
The two tennis stars cited fatigue and injury as the reason why they have chosen not to play in the team event.
The American denied his Canadian opponent Denis Shapovalov the chance to defend his title.
Denis Shapovalov is on track to win his second consecutive Stockholm Open title after beating Felix Auger-Aliassime in the last four.
The Canadian reached the semis after beating the Dutchman in straight sets on Thursday.
There was a lot of emotion displayed during the second day of the season-ending event.
The Canadian was pushed to the limits by his Italian counterpart but managed to pull through.
Daria Kasatkina featured in Russia's 3-0 win over Canada in the Billie Jean King Cup today.
Canada are off to a winning start at the Billie Jean King Cup Finals.
Anett Kontaveit is a top 10 player and heading to the WTA Finals after claiming the title in Cluj.
Simona Halep will have the chance of winning a title on home soil after dismantling Marta Kostyuk in Cluj.
Anett Kontaveit is into back-to-back WTA Finals after another convincing win in Romania.
Marta Kostyuk destroyed US Open champion Emma Raducanu in less than an hour to reach the Cluj semi-finals.
Simona Halep is into the Cluj semi-finals after a dominating display.
Anett Kontaveit is one win away from being a top 10 player after reaching the semi-finals in Cluj.
The Canadian came from behind to beat the Britt in three sets and book his spot in the quarterfinals.
Anett Kontaveit is still in the hunt for the last WTA Finals spot after reaching the Cluj quarter-finals.