Consider the following one stage game, with two players A and B.
There is a pie which is to be divided between the two players. A can offer B any fraction of the cake, which B can accept or reject. If B accepts the offer (say $1-x$), then A gets $x$ and B gets $1-x$. If B rejects the offer, both players get $0$.
As far as the Subgame Perfect Equilibria are concerned, ($1$,accept always) is definitely one such equilibrium. What about ($1-\epsilon$,reject only when $x=1$), where $\epsilon$ is a very small number?