Zych, 27, was placed on waivers for the purpose of his unconditional release, which ends his run with the Mariners after pitching in 70 games over the past three seasons. He posted a 7-3 record and 2.72 ERA in that time, but spent much of the past two years on the disabled list with elbow and shoulder problems and hadn't thrown in a game yet this spring.
Zych and Rumbelow were both contenders for bullpen roles this season, but Zych's shoulder never cooperated and Rumbelow -- the Mariners' No. 15 prospect, per MLB Pipeline -- has been sidelined since his Feb. 24 debut with a neck problem.
The top of the Mariners' bullpen is fairly set, with closer Edwin Diaz, set-up men Juan Nicasio, David Phelps and Nick Vincent, as well as lefties Marc Rzepczynski and James Pazos.
Dan Altavilla would now seem to have a strong hold on one of the final spots in the bullpen, but manager Scott Servais said the next few weeks could determine how things line up. The Mariners will likely open with an eight-man relief crew.
"Looking at those back spots in the bullpen, Altavilla has had a very good spring," Servais said. "We like Chasen Bradford. Casey Lawrence has added some things to what he's doing and is throwing the ball well. We still have competition there with a few guys. We have time and we'll see how it plays out here the next couple weeks."
Rumbelow was acquired from the Yankees in November coming off a strong Triple-A season after returning from Tommy John surgery, but never had a chance to compete this spring once his neck locked up.
"We're starting to have a better idea what it is and having the right treatment there and hopefully it starts calming down and we can move forward," Servais said. "I'm disappointed for Nick. When we acquired him, we were really excited about what he could do in our bullpen. We thought he had a realistic shot to make our team out of camp, but the injury took him off course. We need to get him healthy and I definitely think he'll help us at some point."
Moore and Jiminian are both healthy, but Servais said they were sent down to allow them to continue stretching out as starters since more innings are now being used in Cactus League play for the top rotation contenders.