Looking through the free agent pool, I noticed the following, I'll paste a screenshot.
There's 4 pages worth of these players in their 40s. I can't find any that have stats or have played... ever.
All have similar histories like this...
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06-15-1910 Drafted in the 1910 first-year player draft (Round 12, Pick 16, 192nd overall Pick) by the Boston Red Sox.
01-01-1911 SISA scouting updated ratings (potential): Stuff: 3 (5); Movement: 7 (17); Control: 3 (11).
06-16-1911 Released by the Boston organization.
01-01-1912 SISA scouting updated ratings (potential): Stuff: 4 (5); Movement: 11 (17); Control: 5 (11).
01-01-1913 SISA scouting updated ratings (potential): Stuff: 4 (5); Movement: 11 (17); Control: 5 (11).
01-01-1914 SISA scouting updated ratings (potential): Stuff: 4 (5); Movement: 12 (17); Control: 5 (11).
01-01-1915 SISA scouting updated ratings (potential): Stuff: 4 (5); Movement: 15 (17); Control: 6 (11).
01-01-1916 SISA scouting updated ratings (potential): Stuff: 4 (5); Movement: 16 (17); Control: 8 (11).
01-01-1917 SISA scouting updated ratings (potential): Stuff: 3 (4); Movement: 16 (17); Control: 8 (10).
01-01-1918 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 16 (17); Control: 8 (9).
01-01-1919 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 16 (17); Control: 8 (8).
01-01-1920 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 16 (17); Control: 8 (9).
01-01-1921 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 16 (17); Control: 8 (8).
01-01-1922 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 17 (17); Control: 8 (8).
01-01-1923 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 17 (17); Control: 8 (9).
01-01-1924 SISA scouting updated ratings (potential): Stuff: 2 (3); Movement: 16 (17); Control: 8 (9).
01-01-1925 SISA scouting updated ratings (potential): Stuff: 3 (3); Movement: 16 (17); Control: 9 (9).
01-01-1926 SISA scouting updated ratings (potential): Stuff: 2 (3); Movement: 14 (17); Control: 9 (9).
01-01-1927 SISA scouting updated ratings (potential): Stuff: 2 (3); Movement: 14 (17); Control: 9 (9).
01-01-1928 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 13 (17); Control: 9 (9).
01-01-1929 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 13 (17); Control: 9 (9).
01-01-1930 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 12 (17); Control: 9 (9).
01-01-1931 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 11 (17); Control: 9 (9).
01-01-1932 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 10 (17); Control: 10 (9).
01-01-1933 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 9 (17); Control: 10 (9).
01-01-1934 SISA scouting updated ratings (potential): Stuff: 1 (3); Movement: 9 (17); Control: 10 (9).
Yet they aren't retired. A few have multiple star ratings. All are Middle Relievers. I always figured after a few years of sitting around, they'd just call it a day.