RHP Brendan Donnelly, RHP Juan Rincon, and RHP Scott Elarton filed for Free Agency
Not exactly cornerstone contributors, but let's talk about them.
Brendan Donnelly is the most interesting of the three. The Indians signed him knowing that he'd be rehabbing most of the season, and have only a slight chance of getting anything out of him before the end of the season; even after a pitcher coming off Tommy John surgery is physically able to throw competitively, it usually takes at least a couple months to get back to his former prowess. And while Donnelly doesn't enough service time to file for free agency, the contract he signed stipulated that the Indians would have to essentially release him so that he'd be a free agent along with all the other players with 6+ years of service time.
Whichever team signs him will be getting Donnelly at full health; whether that translates into getting a good reliever is unknown, but I think it would have been a very easy decision to keep Donnelly around had the clause not been in his contract. But with him out on the open market, there's really no reason for the Indians to favor him over any of the other relievers available. Maybe Donnelly would favor the Indians if he had a good experience with the staff, but given that this is his first (and likely last) chance as a viable reliever on the open market, those distinctions probably won't come into play.
I'm a lot less interested in Juan Rincon, who although healthy, has been a train wreck for the past two seasons. Like Donnelly, this is Rincon's first shot at free agency, but while Donnelly can point to his elbow surgery for a reason why he struggled in Boston last season, Rincon can only point to his past success. Juan wants to come back to Cleveland, but I don't see the Indians wanting Rincon back, at least on a major-league deal.
Scott Elarton missed the final three months of the season due to a "non-baseball medical condition," so I don't even want to comment on his baseball future, other than to hope that some time in the future he's ready to play again.