  {\bf{Purpose}:} In this paper, the proton resonance width of the
near-threshold resonance is calculated using two different approaches. The
values of the proton width are used to calculate the low-energy $S$-factor. \\
{\bf{Method:}} First, the proton resonance width is estimated using the mirror
symmetry of the resonance $ {}^{11}{\rm C}(E_{x}=8.70\, {\rm
MeV};\,\frac{5}{2}^{+})$ and the mirror bound state ${}^{11}{\rm
B}(E_{x}=9.272\, {\rm MeV};\,\frac{5}{2}^{+})$. In the second approach, this
width is estimated using the $R$-matrix definition of the observable resonance
width, which is expressed in terms of the $p-{}^{10}{\rm B}$ resonant wave
function calculated in the potential approach and the spectroscopic factor. \\
{\bf{Results}:} Depending on the method chosen, the calculated proton resonance
width varies from $\,1.03 \times 10^{-19}\,$MeV to $\,2.96 \times
10^{-19}\,$MeV. The role of the near-threshold resonance is determined using
fitting of two low-energy $S$-factors from direct measurements [C. Angulo {\it
et al.}, Z. Phys. A {\bf 345}, 333 (1993)] and from the indirect Trojan horse
method (THM) [ A. Cvetinovi\'c {\it et al.}, Phys. Rev. C {\bf 97}, 065801
(2018)]. Within the framework of the $R$-matrix method using the determined
proton resonance widths and the modified THM parameters for six low-lying
resonances, the low-energy $S$-factors were calculated and compared with the
corresponding experimental $S$-factors. The closest agreement with the data is
achieved with the proton resonance widths $1.0 \times 10^{-19}$ MeV when
fitting the $S$-factor from the THM indirect measurements, and $\,1.68 \times
10^{-19}\,$ MeV and $\,2.5 \times 10^{-19}\,$ MeV when fitting the $S$-factor
from [Angulo {\it et al}, Z. Phys. A {\bf 345}, 333 (1993)].\
