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Sassuolo's 11-year stay in Serie A came to an end Sunday after they lost 2-0 to Cagliari and other results they needed to survive the drop went against them.
Frosinone defeated Monza, while Udinese snatched a 1-1 draw with Empoli in the 14th minute of stoppage time.
Matteo Prati and Gianluca Lapadula ensured Cagliari of a place in Italy's top flight with goals in the 71st and 91st minutes in Reggio Emilia.
Sassuolo thought they still had a chance of fighting for survival on the final day of the season, but the aforementioned results ensured they would join Salernitana in Serie B next season.
M'Baye Niang's penalty gave Empoli a 90th-minute lead at Udinese.
But eight minutes later Jacopo Fazzi pulled back Roberto Pereyra just as the Argentine looked set to level for Udinese from close range.
And after a long VAR check, Lazar Samardzic thumped home the equaliser from the spot with the last kick of the game.
That draw and Frosinone winning 1-0 at Monza left second-from-bottom Sassuolo five points from Udinese, who sit one point above Empoli and the relegation zone, with one match remaining.
