Today is the last day for clubs to tender contracts to arbitration-eligible free agent, with the deadline being 12PM ET. If clubs choose not to tender a contract to an arb-eligible player who is unsigned for 2016, that player becomes a free agent.
The logical candidates to be non-tendered, of course, are those players who would likely earn more in arbitration than the club would like to pay. Once the player becomes a free agent, he can sign with anybody, including the club that non-tendered him.
MLBTradeRumors.com has a handy tool for keeping up on the tender/non-tender action here: MLBTradeRumors NON-TENDER TRACKER 2015/2016
There are only four players listed as having been tendered 2016 contracts per the Tracker, but check back today and tonight as it gets filled out.