Claiborne, 28, is a former first-round pick of the Cowboys back in 2012. He played out his rookie contract with Dallas before returning to the team on a one-year, $3 million for the 2016 season.
Last year, Claiborne departed for a one-year contract worth $5 million with the Jets and re-signed with New York to another one-year, $7 million deal back in March.
In 2018, Claiborne appeared in 15 and recorded 57 total tackles, two interceptions, 14 pass defenses, and scored one defensive touchdown.
Enunwa, 26, is a former sixth-round pick of the Jets back in 2014. He played out the final year of his three-year, $1.995 million and made a base salary of $615,000 for the 2017 season before returning to the Jets on a one-year restricted deal worth $2.914 million.
The Jets re-signed him to a four-year, $36 million deal which included $20 million guaranteed on Friday.
In 2018, Enunwa has appeared in 11 games for the Jets and caught 38 passes for 449 yards receiving and one touchdown.