Eligible without an account balance is required to receive the SAR, no question about that.
What isn't 100% clear is whether a terminated participant who has been paid out before the end of the plan year is required to receive the SAR. Standard practice seems to be term with no balance at the end of the year does not get an SAR, but it sort of depends on where you draw the line. The regs just say participant and beneficiary. Many interpret that as "at the end of the year" rather than "at any point during the plan year". I know Janice Wegesin's 5500 Preparer's Manual agreed with the former but I don't think it had a direct citation. Absent anything directly on point, I think either interpretation is reasonable.