The answer to your question is complicated:
* The Baudelaire orphans (Violet, Klaus, and Sunny) are the main characters, and they survive numerous perilous situations throughout the series. However, their lives are filled with constant misfortune and peril.
* The series ends with a somewhat ambiguous resolution, leaving some questions unanswered about their ultimate fate.
It's up to the reader to interpret the ending and decide whether the Baudelaire orphans truly "survived" in the sense of finding lasting happiness and peace.
The series focuses on the theme of resilience and the enduring power of family despite overwhelming adversity.