This is the 14255th most frequent Russian word.
оставшись
"Having remained" or "remaining."
In this context, "оставшись" denotes a past participial construction indicating the subject remained at home before performing another action.
Оставшись дома, он решил привести квартиру в порядок.
Having stayed at home, he decided to tidy up the apartment.
Here, "оставшись" reflects the subject being left alone as a consequence, leading to an emotional state.
Она, оставшись одна, почувствовала лёгкую грусть.
She, left alone, felt a slight sadness.
"Оставшись" here suggests the causal situation of losing the job, preceding the subject's subsequent actions.