Faine is the second of seven draft choices to agree to terms. Long snapper Ryan Pontbriand was on the practice field Monday after agreeing to a five-year deal Sunday.
Although Faine missed seven days of practices, the feeling is he'll be able to participate in Saturday's scrimmage against Buffalo.
"All of us feel a little better because these draft picks have been here extensively during the offseason," Policy said. "They were there and working hard, and, according to Buddy (strength coach Buddy Morris), they're in pretty good shape.
"I think coming it won't be as serious as it has been in the past for rookies (signing) late. You don't want to see it. I'm hoping he can catch up, and I'm hoping he's in a position that he can be utilized to some extent in the scrimmage (against Buffalo) on Saturday."
The final two years of Faine's contract will be voided if he participates in 35 percent of the offensive plays this season. The deal includes an option bonus payable at the start of the NFL offseason next February in addition to the signing bonus.
Policy said that new five-year proposals were put on the table for third-round choice Chris Crocker and Michael Lehan, a fifth-round pick. Talks with fourth-round pick Lee Suggs have slowed because of his rehabilitation from shoulder surgery.
Policy is concerned that Jeffrey Griffin, the agent representing second-round pick Chaun Thompson, hasn't instructed his client to sign. Policy also said that talks aren't going well with sixth-round pick Antonio Garay.
"I think it's important that he (Thompson) get in and that he recognize the quality of the deal that we're offering," Policy said. "He stands to gain a great deal by what this coaching staff has to offer him."
CAMP NOTES: Jamel White is worried about the head injury he suffered during a running drill last Saturday. The Browns running back had his helmet jammed on the bridge of his nose. Although he didn't feel 100 percent, he finished practice. White left the field Sunday after taking a hard hit to the ground.
"I don't feel light-headed. I feel like I'm on a boat," White said. "If I don't feel right, I'm not going to go out there and do something that might hurt myself."