Finding a team willing to take on the public-relations hit of signing Ray Rice will be difficult. But anyone saying it is impossible is ignoring other famous cases of players returning after damaging incidents. Leonard Little, a defensive lineman, played 12 seasons in the N.F.L. after killing a 47-year-old mother in a drunken-driving accident. Donte Stallworth, a wide receiver, played three seasons after pleading guilty to manslaughter for killing a pedestrian in a hit-and-run accident that occurred after he had been drinking. And Michael Vick, the backup quarterback for the Jets, has played six seasons since serving a federal sentence in connection with a dogfighting ring that he participated in.

While no teams have openly showed interest in Rice so far, there are some that may be able to use him, should he prove in a tryout that he is in shape.

ARIZONA: Tied for the best record in the N.F.L., the Cardinals lost the heart of their offense when Carson Palmer had season-ending knee surgery. The team’s defense is playoff quality, but it cannot hold off rapidly encroaching Seattle without more help on offense, where its running backs are averaging an N.F.L.-low 3.1 yards a carry. If Rice could regain his 2012 form, he and Andre Ellington could be enough to earn the team its first division title since 2009.

NEW ENGLAND: The Patriots have shown little commitment to the team’s running backs this season, with LeGarrette Blount leading the team in rushing in Week 12 just a few days after joining it, while Jonas Gray, who rushed for 201 yards in Week 11, did not play a single snap. Coach Bill Belichick is not afraid of controversy and has a tendency to keep players in line, so if he thought Rice could help the team, there would be little stopping him from giving it a try.