Jim Thorpe won the 1500 meter run, the last event of the pentathlon, with a time of 4 minutes 44.8 seconds. Avery Brundage did not finish but was awarded seven points, comparable to a last place finish. Whether he started and did not finish or just didn’t bother to run at all is unclear. Ironically, Thorpe could have finished dead last in the 1500 meters and still won the pentathlon but he probably never considered loafing to save his energy for the decathlon. Brundage finished in sixth place overall, ahead of Hugo Wieslander, who finished fourth in the 1500 meters. The best Brundage could hope for if he came in first, second or third was a bronze medal because, even if he finished dead last, Ferdinand Bie of Norway would have had only 22 points overall as he had only 15 points coming into the 1500 meters where Brundage already had 24. A first place finish would have given Brundage 25. A fourth place finish would have given him 28 points, still good enough for a bronze because James Donahue and Frank Lukeman both finished with 29 points in a tie for third place. The tie was broken by recalculating their results using the method used for the decathlon with the result that Donahue was awarded the bronze medal
According to Wikipedia, Brundage chose not to compete in the final event of the decathlon, again the 1500 meter run, and later regretted the decision. It may be that he also chose not to run the 1500 meters in the pentathlon as well. Perhaps his biographer, Allen Guttman, can shed some light on this but it has been decades since he wrote about Brundage and he may have forgotten the details.
Something that is clearer now is that the Brundage who came in second to Frank Cayou in a track meet held at the University of Illinois on April 28, 1900 probably was Avery. Although still in high school in Chicago, his times were already good enough to compete with college boys.