The 49ers don’t sign big names in free agency?

False.

In the past two years, they’ve signed a slam-dunk, first-ballot Hall of Fame wide receiver, a two-time 1,000-yard running back and a three-time Pro Bowl cornerback.

The more accurate statement: The 49ers don’t sign young big names in free agency.

Since 2012, the 49ers have specialized in signing near-their-expiration-date standouts – Randy Moss (35 when 2012 season began), Brandon Jacobs (30) and Nnamdi Asomugha (32 when ’13 season began) – to team-friendly, one-year deals in hopes of squeezing out a last bit of magic.

The results: Aw. Ful.

Moss had a little-impact 28-catch season, while Jacobs and Asomugha were released before the 49ers’ season ended in 2012 and 2013, respectively. In retrospect, it’s clear that trio had next-to-zippo left: Moss spent 2013 as an analyst; Jacobs retired after a 258-yard season with the Giants last year and Asomugha retired after the 49ers released him Nov. 4.

That trio was preceded by a 2011 free-agent signing – wide receiver Braylon Edwards – with similar echoes. At 28, Edwards was younger but his best days were also in the rearview mirror. The 49ers released him during the 2011 season, he played sparingly with the Jets and Seahawks in 2012 and didn’t play last year.

Given that backdrop, it’s fair to wonder if the 49ers will sign another does-this-guy-have-anything-left player in free agency, which starts Tuesday.

If they do take another swing, below is a list of candidates. In order to make the list, the free agent needed to A) be at least 30 as of Sept. 1 (sorry, Maurice Jones-Drew); B) have made at least one Pro Bowl; C) clearly be in his career twilight (this disqualified the likes of still-highly-productive 30-somethings such as Devin Hester, Charles Tillman and Jared Allen).

Here we go (listed by age):

G Brian Waters, Cowboys

Age on Sept. 1: 37

Dallas isn’t expected to re-sign the six-time Pro Bowler, who missed the last half of 2013 with a torn triceps. The 49ers don’t have pressing interior-line needs with 2012 fourth-round pick Joe Looney and nine-year veteran Adam Snyder under contract.

S Charles Woodson, Raiders

Age on Sept. 1: 37

The eight-time Pro Bowler and 2009 Defensive Player of the Year had a free-agent visit with the 49ers last year after Dashon Goldson signed with Tampa Bay. It’s conceivable they could meet again if Donte Whitner signs elsewhere. Woodson appears to have a little something left: He started 16 games last year and played 1,098 of 1,105 snaps.

CB Champ Bailey, Broncos (released)

Age on Sept. 1: 36

After his release from the Broncos, the 12-time Pro Bowler is a free agent for the first time in his 15-year career. With the 49ers’ futures of CBs Tarell Brown (free agent) and Carlos Rogers (potential salary-cap casualty) uncertain, Bailey could fill a hole while a high-end draft pick finds his way. Like Woodson, Bailey, who played in just three regular-season games in 2013 because of a foot injury, could finish his Hall-of-Fame career at safety.

“My vision is to still play corner, but I’m a little more open-minded about the season I had last year.” Bailey told USA Today. “I’m a corner at heart. If a situation made sense to play safety, then I would consider it.”

S Ed Reed, Jets

Age on Sept. 1: 35

The 49ers were interested in the future Hall of Famer in free agency last year, but were wise to not get too serious. After signing with Houston, Reed was demoted from the starting lineup before he was subsequently released after playing seven games. He finished the season with Jets, who aren’t expected to re-sign him.

QB Michael Vick, Eagles

Age on Sept. 1: 34

Vick, who lost his spot to Nick Foles last year, would like to be a starter somewhere (Oakland?) But if he can’t find a suitor, he could be attracted to a backup role with a contender who could get him a Super Bowl ring. The 49ers figure to look to upgrade from free agent Colt McCoy, last year’s backup to Colin Kaepernick.

DT Kevin Williams, Vikings

Age on Sept. 1: 34

A five-time first-team All-Pro, Williams started 15 games, played 66 percent of Minnesota’s defensive snaps and collected 3.5 sacks last year. The 49ers, however, have a glut of defensive linemen, with three youngsters – Ian Williams, Tank Carradine and Quinton Dial – expected to be at full strength after an injury-marred 2013.

CB Asante Samuel, Falcons (released)

Age on Sept. 1: 33

The four-time Pro Bowl selection is known for his prowess in zone coverage, making him ill-suited for the man-to-man style favored by 49ers defensive coordinator Vic Fangio. In 2013, Samuel, who missed five games, had a career-low three passes defensed.

ILB Jonathan Vilma, Saints

Age on Sept. 1: 32

With inside linebacker NaVorro Bowman possibly sidelined for half the season, the 49ers could address the position in free agency. Vilma, a three-time Pro Bowler, has missed 25 games over the past three seasons (including 15 in 2013) with a troublesome knee. The Saints have announced they won’t re-sign him.