DeCicco made the squad last year as an undrafted rookie free agent and finished second on the team with 17 special teams tackles, most by a Bears player since Corey Graham had 20 in 2007. But DeCicco has been sidelined since the Bears' first preseason game against the Denver Broncos on Aug. 9 with a sports hernia.
He will undergo a minor procedure next week to repair the damage, according to a league source. Recovery time from the surgery is expected to be 3-4 weeks.
DeCicco is expected to receive an injury settlement from the Bears, which means he would not be able to re-sign with the team until after the duration of the settlement, plus an additional six weeks, per the new collective bargaining agreement. That means DeCicco's best option might be to sign elsewhere when the injury settlement expires.
Bears linebacker Bob Babich talked about DeCicco before the Bears' decision to waive him.
"Dom was banged up (before the groin injury), so he wasn't moving as well as we've seen him in the past," Babich said after practice Tuesday. "But Dom is good mentally. (But) missing these days has hurt him."
Crump, who the Bears originally waived on Sunday, is an undrafted rookie free agent out of Western Illinois.