The word 'whomsoever' is rarely used in everyday conversation but may appear in formal writing. Whomsoever shall be found guilty, ought to be punished accordingly.
Pro Tip 2/3
Emphasis on Any
'Whomsoever' is used when emphasizing that anyone at all could be chosen or affected. This reward shall go to whomsoever solves the mystery first.
Pro Tip 3/3
Impersonal Constructs
It's often found in expressions that need to be impersonal, like 'To whomsoever it may concern'. To whomsoever it may concern: the lost belongings have been found.