After the 2005 season, Aybar was a candidate to start at third base for the Dodgers in 2006. However, in the offseason, the Dodgers signed free agent and former batting champion Bill Mueller as their starting third baseman. After they also signed Ramón Martínez to join Óscar Robles in being the primary backups, Aybar found himself out of a job. His .216 batting average during spring training did not help his cause either.
On May 12, 2006, Aybar received another opportunity to be the starting third baseman when Mueller was placed on the 15-day disabled list for arthroscopic knee surgery, he was recalled from the Dodgers Triple-A affiliate, the Las Vegas 51s.
Atlanta Braves
On July 28, 2006, he was traded to the Braves along with relief pitcher Danys Báez for infielder Wilson Betemit.[1]
On April 18, 2007, Aybar was suspended indefinitely for unknown reasons. He was first suspended on April 15 for three games for failing to show up for treatments for an injured hand. This was a rare move by the Braves organization, and Aybar's lack of participation caused third baseman Chipper Jones to remark "I didn't even know he was still on the team." It was revealed on April 19 that Aybar, according to his agent, had been struggling with "drinking and drugs." He had not been heard from for some time and failed to report to New York for a meeting with major league officials Friday, April 20, according to the Atlanta Journal-Constitution. It was later revealed that Aybar was seeking help at a drug treatment facility.[2] Aybar was removed from the suspended list on August 4 and was sent to the minor leagues to get in shape for being called up. However, on August 14, he underwent season-ending surgery for a stress fracture in his right hand.
Tampa Bay Rays
On January 17, 2008, Aybar was traded along with Chase Fontaine to the Tampa Bay Rays for Jeff Ridgway.[3] On March 24, 2008, it was announced that he would be the starting third baseman for the 2008 Tampa Bay Rays. He held this position until Evan Longoria was called up early in the season. Aybar then took the role of utility player. He finished the season batting .253 with 10 home runs and 35 RBI in 95 games. In the field, Aybar started 40 games at third base, 18 at first base, 14 at designated hitter, six at second base, and two at shortstop.[4]
He hit a home run in the seventh and deciding game of the ALCS, a 3–1 Rays victory that sent the franchise to the World Series for the first time.
On February 18, 2009, Aybar signed a two-year, $2.6 million contract with the Rays to avoid arbitration.[4]
On December 3, 2010, Aybar was non-tendered by the Rays, making him a free agent.[5]
Yuma Scorpions
Aybar was selected to play for the Edmonton Capitals in the North American League on February 11, 2011. However, he was released by the Capitals due to the Canadian government not granting him a visa. He later joined the Yuma Scorpions in the same Independent league, which was managed by Jose Canseco. In 13 games he hit .302/.388/.372 with 0 home runs and 3 RBIs.
Delfines de Ciudad del Carmen
On March 15, 2012, Aybar signed with the Delfines de Ciudad del Carmen of the Mexican League. He was released on April 22. In 7 games he struggled mightily going 4-24 (.167) with 0 home runs and 1 RBI.
Leones de Yucatán
On March 27, 2015, after 3 years of inactivity Aybar signed with the Leones de Yucatán of the Mexican League. He was released on June 9. In 35 games he hit .282/.353/.427 with 3 home runs and 17 RBIs.
Vaqueros Laguna
On June 12, 2015, Aybar signed with the Vaqueros Laguna of the Mexican League. He was released on July 11. In 21 games he hit .314/.402/.514 with 4 home runs and 12 RBIs.
2009 World Baseball Classic
In the 2009 WBC (World Baseball Classic), the Dominican Republic team faced the Netherlands in the first round. After the game went into extra innings, the Dutch team scored on an error made by Aybar, eliminating the heavily-favored Dominican team.
Aybar has been arrested on multiple occasions for assaulting his wife. On January 31, 2008, he was arrested on domestic violence charges for assaulting his wife in the Dominican Republic.[7] In 2010, Aybar was convicted and sentenced to three months in prison for assaulting his wife and violating a restraining order. She had suffered serious injuries and spent some time in an ICU while in critical condition.[8] In June 2011, Aybar was arrested again for allegedly assaulting his wife. According to the police report, Aybar, who has also battled alcohol problems, was found "extremely intoxicated" at the front entrance of the SeaTac Hilton hotel. Police documents stated they went to Aybar's room, where his wife was crying and holding a bloody towel to her face and had a cut lip and an abrasion on her forehead and cheek.[9]