Taiwan's Eastern Broadcasting Corp reported that Tsao Wei-ling called out "Here I am" as rescuers dug through to find her.
A male survivor was pulled out conscious from the sixth floor section of the folded 17-story building, according to a notice posted at a rescue information center on site.
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More than 100 people are believed to be still buried in the collapsed building from a disaster that struck during the most important family holiday in the Chinese calendar - the Lunar New Year holiday.
The government in Tainan, the worst-hit city, said that more than 170 people have been rescued from the 17-story building, which folded like an accordion after the quake struck.
The death toll from Saturday's powerful 6.4-magnitude quake in south Taiwan stood at 36. 34 of which were from the building collapse in Tainan city, and two other people died elsewhere in the city.
Rescuers said Tsao was found under the body of her husband, who had shielded her from a collapsed beam, Taiwan's government-run Central News Agency reported. Her husband and 2-year-son were found dead, while five members of her family remained unaccounted for, it said.
Earthquakes frequently rattle Taiwan, but most are minor and cause little or no damage, though a magnitude-7.6 quake in central Taiwan in 1999 killed more than 2,300 people.
The spectacular fall of the high-rise, built in 1989, raised questions about whether its construction had been shoddy.
Tainan's government said the building had not been listed as a dangerous structure, and Taiwan's interior minister, Chen Wei-zen, said an investigation would examine whether the developer had cut corners.
The extended Lunar New Year holiday officially started Monday, but celebrations were subdued and both President Ma Ying-jeou and President-elect Tsai Ing-wen canceled the handing out of envelopes of cash in their hometowns, a holiday tradition for Taiwan's leader.
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