During the Battle of the Rubble, the Infinite Spoils first housed Thel 'Vadamee and his crew when they had been captured by the Kig-Yar. However, the Elites broke free of their prison and captured a Kig-Yar transport.
Later, the Infinite Spoils was boarded by a group of humans under the command of Lieutenant Jacob Keyes. The humans eliminated most of the Kig-Yar crew and obtained information from its computers. However, at the same time, Thel 'Vadamee and his Sangheili also boarded the Infinite Spoils. After a brief run-in with the Sangheili, the humans quickly left the Infinite Spoils leaving it to the Elites, who used it to attack and destroy the mass drivers on the Rubble.
The Infinite Spoils remained under Thel 'Vadamee's command for the duration of the battle. What became of it afterward is unknown. 
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