There are a number of compound pronouns that seem to have two forms. I can’t tell the difference at all between them, and the O.E.D. doesn’t seem to be clear on it either.
In particular, “whoever” – with its objective and genitive cases “whomever” and “whosever” – seems to be completely identical to “whosoever” – along with “whomsoever” and “whosesoever”.
What’s the difference?
No difference.
Partridge in The Concise Usage and Abusive calls whosoever “archaic.”
Fowler in the second edition of Modern English Usage calls whomsoever “literary,” whosesoever “archaic,” and whosoe’er and whomsoe’ver “poetic.”
Just another dreary case of elegant variation. 
I certainly use ‘whosoever’, and so would quibble the ‘archaic’ classification. (Of course, it’s reduced by dialect/accent to ‘hoo’sver’, but I’m serious in saying that it’s still commonly used.)
Perhaps it’s your dialect then. After all, I understand they still say thou and thee in Yorkshire, but that doesn’t mean those expressions are not considered obsolete in the language at large.
I don’t think I’ve heard anyone say ‘whosoever’, though I often do hear ‘whatsoever’. It seems to be useful for emphasis.
So, what changed? Why was “so” dropped?
Eliding unnecessary syllables is a long-standing habit of the English language. I don’t know whether or why it applies in this particular case, but the general pattern can be found in many other examples.