Worker [topic-は] advance-notice without [state-に] fired-be [nominalizer-こと] [topic-は] not-exist.
事前通知なしに ('without advance notice') uses なし ('without') as a suffix. 解雇される ('to be fired') is the passive of 解雇する. ~ことはない ('there is no case of') means it doesn't happen — a statement of rights.