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A continuum is a compact connected metric space. A non-empty closed subset$B$ of a continuum $X$ does not block $x\in X\setminus B$ provided that theunion of all subcontinua of $X$ containing $x$ and contained in $X\setminus B$is dense in $X$. We denote the collection of all non-empty closed subset $B$ of$X$ such that $B$ does not block each element of $X\setminus B$ by$NB(F_1(X))$. In this paper we show some properties of the hyperspace$NB(F_1(X))$. Particularly, we prove that the simple closed curve is the uniquecontinuum $X$ such that $NB(F_1(X))=F_1(X)$, given a positive answer to aquestion posed by Escobedo, Estrada-Obreg\'on and Villanueva in 2012.

The hyperspace of non blockers of $F_1(X)$