We provide estimates for the spectral radii of an $n\times n$ sparse non-Hermitian random matrix $Z$ with general entries in the regime $p=d/n$ where $0<d<1$ is fixed. Utilizing the structural results of (Łuczak, '90), we show that the spectral radius $ρ(Z)$ is $0$ with probability converging to some nonzero value, and satisfies the inequality $(φ(n))^{-1}\leq ρ(Z)\leq φ(n)$ in the asymptotic sense for any function $φ$ satisfying $\lim_{n\to\infty}φ(n)=\infty$ with the remaining probability.