Summary: In the paper, we consider the limit behavior of partial-sum random field (r.f.) \(S_{\mathbf{n}} \left( t_1, t_2; X \left( b\left( \mathbf{n}\right)\right)\right) =\sum_{k=1}^{[n_1 t_1]} \sum_{l=1}^{[n_2 t_2]} X_{k,l}\left( b\left( \mathbf{n}\right)\right)\), where \(\left\{ X_{k,l} \left( b\left( \mathbf{n}\right)\right)=\sum_{i=0}^{\infty} \sum_{j=0}^{\infty} c_{i,j} \xi_{k-i,l-j}\left( b\left(\mathbf{n}\right)\right),k,l\in \mathbb{Z}\right\} ,n\geqslant 1\), is a family (indexed by \(\mathbf{n} = (n_1, n_2), n_i \geqslant \mathbf{1})\) of linear r.f.s with filter \(c_{i,j} = a_i b_j\) and innovations \(\xi_{k,l} (b(\mathbf{n}))\) having heavy-tailed tapered distributions with tapering parameter \(b (\mathbf{n})\) growing to infinity as \(\mathbf{n} \rightarrow \infty\). In [Part I, V. Paulauskas, Lith. Math. J. 61, No. 2, 261–273 (2021; Zbl 1475.60095)], we considered the so-called hard tapering as \(b (\mathbf{n})\) grows relatively slowly and the limit r.f.s for appropriately normalized \(S_{\mathbf{n}}(t_1 ,t_2;X(b(\mathbf{n})))\) are Gaussian. In this paper, we consider the case of soft tapering where \(b (\mathbf{n})\) grows more rapidly in comparison with the case of hard tapering and stable limit r.f.s. We consider cases where the sequences \(\{ a_i\}\) and \(\{ b_j\}\) are long-range, short-range, and negatively dependent.