What happened to Emily Bennett after Katherine was "death" ??

あなた mean dead? She lived her life.

Damon would protect Emily's descendants and Emily would use her grimoire to protect Katherine によって entombing her with 26 other ヴァンパイア under the old Fell's Church. She was later burned at the stake によって the Founding Families and her possessions, including her grimoire, were taken and buried in Giuseppe Salvatore's grave. Damon rescued Emily's children when the townspeople came for her.Wikipedia, section Emily Bennet