What's the rule for choosing between "whoever" and "whosoever" as a subject for a sentence? Even if they have the same semantics (of which I'm not sure), I'm assuming there some contextual or stylistic considerations for choosing one over the other.
Whosoever is, according to ODO,
formal term for whoever.
So you should/could use it in more formal situations.
The Bible commonly uses whosoever (because it is 'archaic' and formal):
For whosoever will save his life shall lose it: but whosoever will lose his life for my sake, the same shall save it.
Holman Christian Standard Bible, Luke 9:24
Of note is the extra syllable, if you wanted to write a poem or something in a particular rhythm.
They're semantically indistinct. You may find slight differences from dictionary to dictionary but native speakers won't be able to agree upon any meaningful difference beyond a stylistic difference. "whosoever" is very ritualistic and eldritch. If you were writing a fantasy novel like Lord of the Rings, or anything dealing with rites and rituals of a cult or extinct religion, it may be better to use "whosoever". A sentence like "whosoever wields this sword shall be cursed" rings better than "whoever" would. It would be very, very weird to use "whosoever" in normal speech under any circumstances, whether in conversation or instruction or giving a speech.
As other people have mentioned, "whosoever" and "whoever" seem to ne generally interchangeable, and "whoever" is more common, but "whosoever" sounds more formal or old-fashioned.
I did think of one grammatical context where "whosoever" seemed like it would be more common to me, and the Google Ngram Viewer seems to confirm my guess: the emphatic expression "anyone whosoever" seems to be a bit more common than "anyone whoever" (however, it's pretty close, and both expressions are uncommon):
(Actually, "anyone whoever" seems to sometimes be a typo or OCR error for "anyone who ever", so the true difference in frequency might be a little greater than it appears here.)
Here is an example of how "anyone whosoever" is used as an emphatic version of "anyone":
It has been further agreed in the said assembly, that if hereafter the commons of the upper end should need to be enlarged, in order to procure more pasturage for the cattle, all the said inhabitants (s'y porterons) shall help in doing the same, as this day they bind themselves to do for the lower end, always without prejudice to anyone whosoever.
- United States Supreme Court Reports, Volume 11, "Chouteau v. Eckhart", p. 348
While this sounds very dry and formal, it really wouldn't sound any more natural to use "anyone whoever" in this context; in fact, my feeling is that it would sound incomplete for whatever reason.
Similarly, "anything whatsoever" sounds more natural to me as an emphatic form than "anything whatever".
Actually, "anyone whatsoever" is also used and is a good deal more common than both "anyone whosoever" and "anyone whoever":
Since the question asked about use as a subject specifically, I found the following example:
Though anyone whosoever could possess a seal, yet these private persons' seals had no other credit than to-day is accorded to a personal signature or seal.
(It's not really clear to me what the ultimate origin of this sentence is. It occurs in a footnote of a document by Herbert F. Krucker, and preceded by the statement "In VII Wigmore, Evidence § 2161 (3d ed. 1940), page 634, Wigmore quotes the following with approval", but I can't figure out who Wigmore is quoting with approval.)