Das OED schreibt hierzu:
"2. Used with generalizing or emphatic force after words or phrases preceded by how, what, which, whose, etc."
At all; in any way: "Space to breathe, how short soever" (Ben Jonson).
in any way at all: used to emphasize or make less precise a word or phrase, usually in combination with what, where, when, how, etc., or else separated by intervening words Compare whatsoever
"attempting to moderate the grief of her friend by philosophical observations on the many disappointments to which human life is daily subject, which, she said, was a sufficient consideration to fortify our minds against any accidents, how sudden or terrible soever." (The History of Tom Jones)
"for, by the fundamental laws of the realm, it is capital in any person, of what quality soever, to make water within the precincts of the palace." (Gulliver's Travels)
"The causes and motives of seditions are, innovation in religion; taxes; alteration of laws and customs; breaking of privileges; general oppression; advancement of unworthy persons; strangers; dearths; disbanded soldiers; factions grown desperate; and what soever, in offending people, joineth and knitteth them in a common cause." (Essays, Sir Francis Bacon)