"You always hold out hope, but he made a decision and I wish him well," Rangers manager Jeff Banister said.
Shawn Tolleson moved into the closer role May 20 and hasn't given it up. Since then he was 12-for-12 in save opportunities, had a 1.47 ERA and held opponents to a .206 batting average entering play Friday.
Feliz's departure takes away a safety net for the Rangers, but Tolleson said he wasn't looking at it that way.
"Whoever is throwing good, that's how it happens," Tolleson said. "That's how it happened to me. If Neftali was still a part of our bullpen, I still would have felt confident I would have the closer's role. I miss Neftali. He is a good pitcher and good teammate. He had a lot of knowledge and a lot of good things to say. He was a good guy to talk to."
The Rangers entered Friday's game against the Padres with a bullpen ERA of 4.30, the highest in the American League. But there is some hope that stability is settling in behind Tolleson with right-handers Tanner Scheppers and Keone Kela and left-hander Sam Freeman taking over the setup roles.
That leaves Spencer Patton in middle relief, Ross Detwiler as the second left-hander and Anthony Bass and Anthony Ranaudo as the long relievers.
Entering Friday, Rangers relievers had a 3.66 ERA in their past 21 games. Scheppers had not been scored upon in his past nine games while Kela and Freeman had not allowed a run in their past five outings.
"I like where Tolleson is right now," Banister said. "I like where Scheppers is at and how he is pitching, the aggressiveness of Sam Freeman and his confidence. ... Keone is getting stronger and settling in and Patton has shown up well. He gives us an opportunity to have somebody out there in the sixth inning and even the seventh if Keone is down. I like the confidence we have in Bass in long relief. Detwiler is continue to work through his challenges and settling in as the second left-hander."
Ranaudo should be starting every fifth day at Triple-A and the Rangers still view him as a starter. But right, now the Rangers don't need a fifth starter until after the All-Star break so Ranaudo is giving them an extra arm in the bullpen.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.