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

You mean dead? She lived her life.

Damon would protect Emily's descendants and Emily would use her grimoire to protect Katherine por entombing her with 26 other vampiros under the old Fell's Church. She was later burned at the stake por 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