On the General Construction for Kleene star in Context-Free Language


I have a first edition of 'Elements of the Theory of Computation' by
Lewis and Papadimitriou, which is published in early 1980s. In this
edition, the author said that we can construct Kleene star operation
in context-free language (CFL) in this way.

Let G = (V, T, P, S) be a CFG where S is a starting symbol. Then
adding another rule that 'S -> SS | \epsilon' generates Kleene closure
of the language that G generates.

I have seen many recent books that present a different construction.
Nowadays, they introduce a new start symbol S_1 and add a new rule
'S_1 -> S S_1 | \epsilon.' It means that there exists a counterexample
that simply adding 'S -> SS | \epsilon' cannot generates Kleene
closure for a certain language. I have tried to find a counterexample
but in vain. Is there anyone who knows the counterexample?

.

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