Rumor has it that the great Shakespeare used the word whosever in his work, and indeed he did. (That’s also true of Mark Twain and the Bible.) I don’t have much to say about Shakespeare—we all love his work (and that goes for Twain and the writers of the Bible, too)—but I do know that in modern language, whosever is not a standard relative pronoun—even though my spell checker doesn’t mind it.
Whosever toys are on the floor had better put them away should be Whoever’s toys are on the floor had better put them away. More to the point, Whoever’s writing the spell checker software and I disagree on standard relative pronouns.
I’ve even seen this spelled whoseever. Really.