2 The leafs & the islanders
No teams in the NBA have ever come back from a 3-o series deficit in any NBA 7 game series including the Finals.
There were no teams ever came back from 3-0 deficit. There were some who forced a game 7 though. However, there were 7 teams to win a playoff series from 3-1 deficit.
The 2015-16 Cleveland Cavaliers overcame a 3-1 deficit to the Golden State Warriors in the NBA Finals
The last time two teams rematched in the Stanley Cup Finals was in 2009 when the Pittsburgh Penguins defeated the Detroit Red Wings in 7 games. In 2008 Detroit had defeated Pittsburgh in 6 games. It was the first back-to-back rematch since 1984 between the Edmonton Oilers and New York Islanders, who likewise split their two meetings (NYI-1983, EDM-1984). In all, Finals teams have rematched for the Stanley Cup nine times since 1932.
The 2015-16 Cleveland Cavaliers overcame a 3-1 deficit to the Golden State Warriors in the NBA Finals
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The last few teams to have back to back are the Redwings, Penguins in the 90's and the Oilers and Islanders in the 80's. The Islanders won 4 years in a row as well as the Canadiens 4 in a row in the 70's.
The Boston Red Sox baseball team came back from 3-0 to defeat the New York Yankees in the AL Championship series in 2004, 4 games to 3. The 1974-75 New York Islanders came back from a 3-0 deficit against the Pittsburgh Penguins to win the series, and almost did it again against the Philadelphia Flyers, tying that series 3-3, but losing game 7. The 1941-42 Toronto Maple Leafs actually came back from down 3-0 in the Stanley Cup Finals against Detroit, coming back to win the Stanley Cup. And of course the 2009-10 Flyers against the Boston Bruins.
Montreal Canadiens came back from a 3-1 deficit in 2010
Only three teams-Boston in 1969, Portland in 1977 and Miami in 2006-have overcome an 0-2 deficit to win the title.
No one has the cup. I'm pretty sure that after the summer and everyone has had their turn with it, it goes back to the place that it's stored until the Stanley Cup Finals, then it attends games 5-7.
1979 New York Islanders & 1942 Toronto Maple Leafs