And then he showed why he might.
After muffing a chance badly in the first half, Thigpen had a 32-yard punt return midway through the fourth quarter to set up Miami's go-ahead score, and the Dolphins beat the St. Louis Rams 14-13 on Thursday night in the preseason finale for both teams.
"The first half, I felt like I was kind of out of it," Thigpen said. "I didn't have a rhythm going and I knew I had to pick it up. The second half, I came out with a different attitude and knew I had to make some plays."
Matt Hazel caught a 22-yard touchdown pass from Seth Lobato with 6:15 left for the Dolphins, who rallied with two TDs in the final quarter. Daniel Thomas, making his preseason debut and playing with the belief his spot on the roster wasn't secure, had a 5-yard touchdown run for Miami.
Michael Sam was in on six tackles for the Rams, and Ethan Westbrooks had a sack for St. Louis. They're among the candidates for one of the final spots on St. Louis' defensive line, a particularly deep position for the Rams.
"I'm very confident that I'll be playing on a NFL roster this fall," said Sam, the NFL's first openly gay player.
He plans to go watch his former college teammates at Missouri play Saturday while the Rams decide his fate.
"I think he can play in this league," Rams coach Jeff Fisher said, "as can some of the other guys on this team who had good preseasons."
A week ago, the Rams lost their starting quarterback. If nothing else, now they may have some confidence in the new backup.
Davis came into St. Louis' training camp as an afterthought, buried at the bottom of the quarterback depth chart. He's now the backup behind Shaun Hill, who became the starter when Sam Bradford was lost for the season with a torn ligament in his left knee.
Given the way he's played in the preseason, Davis might be ready. He completed 12 of 19 passes, albeit largely against second- and third-stringers, and finished the preseason 39 of 63 for 534 yards with four touchdowns and one interception.
Both teams held out plenty of regulars, standard for teams in the final preseason game. Rosters will be cut to 53 by Saturday afternoon, meaning about 700 players in uniform around the league on Thursday night will be either headed to practice squads or looking for new teams shortly.
"Jobs are open," Dolphins coach Joe Philbin said. "That's why we're here."
Thigpen is one of those whose immediate future is a great unknown.
Late in the first half, Thigpen muffed a punt at the Miami 28, kicked the ball while trying to pick it up, and wound up falling on it at the 12 -- a loss of 16 yards.
But in the fourth, after catching another punt deep in Miami territory, Thigpen darted to his left, then up the middle, made a couple of Rams miss and wound up breaking a runback to nearly midfield, drawing plenty of helmet-slaps from teammates.
"You never want to see a player that's going to cost you 18 yards of field position, but sometimes these things happen," Philbin said. "So he buckled up his chin strap a little tighter, went back to work and made a good play and put us in great field position. That certainly says a lot about him."
Lobato completed 12 of 25 passes for 147 yards for Miami. Matt Moore, who started Thursday and will open the season as Ryan Tannehill's backup, completed five of eight passes for 38 yards in relatively limited action.
Trey Watts had 51 rushing yards on 13 attempts for the Rams. ... Dolphins K Caleb Sturgis, who has been hurt for much of the preseason, warmed up well, Philbin said. Sturgis had both Miami extra-points.