<p>We investigate whether black holes can persist through the bounce with a minimal scale factor in a non-singular cosmology, whereby black holes from a previous contracting phase survive into the current expanding one. We do so by studying a generalized McVittie spacetime which embeds a spherically symmetric black hole in a positive spatial curvature bouncing FLRW cosmological background within the modified theory of teleparallel new general relativity. There are no further assumptions on the spacetime (e.g., on the form of the scale factor) initially, and the local evolution is derived from the field equations of the theory, utilizing a perturbative scheme which is valid “near the bounce". To leading order we obtain a simple bounce solution similar to that in general relativity for a closed FLRW model with a positive cosmological constant, but in which the curvature term in the Friedmann equation is re-normalized within new general relativity. Qualitatively the minimum of the bounce at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(t=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> changes, but near the bounce the evolution remains symmetric. The central inhomogeneity evolves at higher perturbative orders, where the details depend on the arbitrary constants of the perturbative solution. Hence the evolution of the local horizon during the bounce changes qualitatively, where the effects depend on the signs of the perturbation, and the symmetry across the bounce is disrupted due to a linear term.</p>