、。
After mother suddenly died, father took care of me all by himself.
Literal
Mother [subject-が] suddenly-died after, father [subject-が] alone [by-で] me [gen-の] care [obj-を] did-for-me.
一人きり stacks 一人 ('one person, alone') with the suffix きり ('only, nothing but'), giving 'all alone, by oneself, with no one else.' Stronger and more emotionally loaded than 一人で alone. ~た後 ('after X happened') is the standard 'after' construction, attaching to the past form of a verb. The whole sentence has a quietly emotional flavor.