On the last day of the event's group stage, Arvidsson replaced Maria Kirilenko, who pulled out of the competition on Thursday with an upper respiratory illness. Arvidsson and Zheng had no chance of advancing to the semifinals.
In Group Serdika, Taiwan's Hsieh Su-wei defeated Daniela Hantuchova 6-1, 0-6, 6-4 in the last match of the day.
Hsieh, who arrived in Sofia with a career-best ranking at No. 25 after finishing 2011 at No. 172, avenged her loss to the Slovak in the PTT Pattaya Open semifinals in Thailand in February. Neither player could advance after Caroline Wozniacki and Italy's Roberta Vinci secured the group's two semifinal berths.
On Saturday, the top-seeded Wozniacki will play Pironkova, while Petrova will face Vinci.
"I need to recover fast because it will be a challenging game tomorrow. Roberta (Vinci) is always giving her opponent a hard time with her slice," Petrova said.