My understanding is that the W-4 goes to your employer so they can withhold the correct taxes and prepare your year end W-2. As Social Security is not taxable by itself, but only in light of income from employment (W-4 to employer) or self employment (quarterly estimated taxes), I don't see a reason why you would. But I'm no accountant, tax attorney, or anything like that so you might call and ask about your specific situation.
Most likely if it has to do with a case there
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