West, 27, originally signed on with the Chiefs as an undrafted free agent out of Abilene Christian back in 2014. He returned to the Chiefs on an exclusive rights contract in 2016 before agreeing to a three-year, $4.2 million contract.
West was set to make a base salary of $1.45 million for the 2018 season when the Chiefs released him. The Jets signed him to a contract in August but waived him as they trimmed their roster down to the 53-man limit.
In 2017, West appeared in 13 games for the Chiefs and rushed for 72 yards on 18 carries (4 YPC) to go along with 27 receptions for 150 yards receiving and four total touchdowns.
Allen, 22, signed on with the Panthers as an undrafted free agent back in April. He began his college career at Texas A&M before transferring after two seasons and joining Houston for the 2017 season.
Allen was waived coming out of the preseason before the Panthers added him to their practice squad last week, but elected to waive him last week in favor of DT Kendrick Norton.
During his college career, Allen threw for 4,283 yards while completing 61.7 percent of his passes to go along with 37 touchdowns and 18 interceptions over the course of three seasons and 24 total games played.