By Chris Emma—

(CBS) Grasping the star of his past with the hopes for his future, Victor Cruz arrived in Chicago a humble man.

Cruz was an incredible story in New York, an undersized undrafted player from just down the road who became one of the league’s top receivers. He had three seasons of strong production from 2012-’14, but three lost years riddled by injury have followed.

Just like that, at the age of 30, Cruz was sent to search for new opportunity. He joined the Bears this past offseason with a one-year deal and plenty of motivation.

“The strive for perfection,” Cruz said. “I’m not done playing this game by any means, and I want to continue to prove that, continue to perform.”

There are many like Cruz with something to prove on this Bears roster, which will ultimately be cut down to 53 men in less than two weeks. General manager Ryan Pace has stocked his roster with low-risk investments whio could potentially offer a good return.

Veterans like cornerback Prince Amukamara, receiver Kendall Wright and defensive lineman Jaye Howard signed with the team on one-year deals, hoping to find their old form. There are those like defensive backs Kyle Fuller and Johnthan Banks who were once drafted highly and now hope to hold a place in the league. And then there are defensive lineman Akiem Hicks and linebacker Jerrell Freeman playing on bargain deals and aiming to get a major pay day.

While this is a team game, it’s also a cruel business that creates these internal motivations. The holdouts of NFL stars Aaron Donald and Le’Veon Bell this preseason seemed justified as Odell Beckham Jr. was writhing in pain in Monday’s exhibition game. Amid contract talks with the Giants, Beckham may have dodged a bullet with what’s currently being called an ankle sprain.

Then there’s a player like the Bears’ Mike Glennon, whose three-year deal is essentially a one-year offer to prove he’s an NFL starting quarterback. Second chances to start are rare in this league. Third chances are even fewer.

Players will tell you that every contract is a one-year deal.

“Every year, you’re looking to get replaced by somebody who’s coming in, who’s younger, and that’s a great thing,” said Chicago cornerback Marcus Cooper, who lost his place in Kansas City last offseason and was traded to Arizona. “It brings in competition and allows for the veterans to continue to step up and try to get better every year. It allows for complacency not to ever set in.

“You have to take that one-day mentality, whether it’s a three-year deal, a five-year deal, a one-year deal. Every day is an important day for you.”

Cooper signed a three-year deal with the Bears worth up to $16 million, but only half of that guaranteed. He had three interceptions as a rookie in 2013, then zero the next two seasons. In 2015, he was inactive for six games and then became expendable to the Chiefs. He arrived with the Cardinals and posted a career-best four interceptions in 2016, earning a contract with the Bears in March.

Amukamara is hoping for a bounce back of his own. The Giants didn’t re-sign him after 2015 after five seasons of quality work. He joined the Jaguars on a one-year deal and had just six pass-breakups and zero interceptions in 12 starts in 2016. Jacksonville would let Amukamara walk, and Chicago offered him another one-year deal.

“I don’t want to start bouncing around teams,” Amukamara said during mini-camp. “I want to find a home somewhere soon, what I did in New York. I’m trying to give this team everything I’ve got.

“Every one-year deal is a prove-it deal for the player. That’s just my mindset this year.”

Added Cruz: “Focus on the now, be in the now, live in the now, so you don’t look ahead or you don’t look forward. Focus on being the best player you can be in the moment and everything else will take care of itself.”

Now entering his third season as general manager with mostly his own personnel, Pace has full ownership of this Bears roster. It’s a team hoping to identify the key pieces to move forward with in its future. Looking ahead, only guard Kyle Long has a contract promised in 2021, and the newest rookie class is the only group signed to join him in 2020.

Chicago possess a projected $18.3 million in top-51 cap space available entering this season, per Spotrac, and the opportunity to open the books in free agency for the right pieces around a young core moving forward. Pace has maneuvered carefully in building this roster, ensuring he wouldn’t handcuff the team with a bad contract during potential years of contention. For now, he’s asking players to prove worthy of staying around.

The next Bears player likely to receive a long-term deal is Hicks, who forced Pace’s hand with a breakout season in the first of a two-year, $10-million deal worth $5 million guaranteed. Hicks recently hired venerable agent Drew Rosenhaus as his new representation, and sources confirmed that discussions with the Bears have taken place. The 27-year-old Hicks could command a four-year deal to stay in Chicago, a place that he now considers a comfortable home.

Freeman is in a similar place to Hicks after a stellar first season with the Bears. He was graded as the top inside linebacker in the NFL last season by Pro Football Focus, with his 93.8 overall grade trailing only Donald and Khalil Mack. But it was a season shortened by four games after being suspended for violating the league’s policy on performance-enhancing drugs.

Freeman is now 31 and in the second season of a three-year, $12-million deal, with half of that guaranteed. His place in Chicago will garner a thorough evaluation this season. Freeman certainly has more he hopes to prove.

“I want to be known as one of the top linebackers in the league,” he said.

While a linebacker on the wrong side of 30 won’t get a major pay day, Freeman can solidify a place leading this Bears defense for the next several years. An unexpected drop-off would put that all in question.

There’s always something to prove in this league. Players unite as a team with the common goal of winning a championship each season, but the personal incentives are a real motivation for players. Pace will gladly reward those low-cost investments who prove his belief right.

Money means security in a game and business that can take everything away in an instant. It feels like everyone is playing on a one-year deal.

“Just embrace what’s in front of you and control what you can control,” Cruz said. “That’s the biggest thing I’ve learned in this league. You can’t control everything.”

Chris Emma covers the Bears, Chicago’s sports scene and more for CBSChicago.com. Follow him on Twitter @CEmma670 and like his Facebook page.