  The observed breakBRD ("break bulges in red disks") galaxies are a nearby
sample of face-on disk galaxies with particularly centrally concentrated star
formation: they have red disks but recent star formation in their centers as
measured by the D$_n$4000 spectral index (Tuttle & Tonnesen 2020). In this
paper, we search for breakBRD analogues in the IllustrisTNG simulation and
describe their history and future. We find that a small fraction (${\sim}4\%$
at $z=0$; ${\sim}1\%$ at $z=0.5$) of galaxies fulfill the breakBRD criteria, in
agreement with observations. In comparison with the mass-weighted parent
IllustrisTNG sample, these galaxies tend to consist of a higher fraction of
satellite and splashback galaxies. However, the central, non-splashback
breakBRD galaxies show similar environments, black hole masses, and merger
rates, indicating that there is not a single formation trigger for inner star
formation and outer quenching. We determine that breakBRD analogue galaxies as
a whole are in the process of quenching. The breakBRD state - with its highly
centrally concentrated star formation - is uncommon in the history of either
currently quiescent or star-forming galaxies; however, approximately 10% of
$10^{10} < M_\ast/M_{\odot} < 10^{11}$ quiescent galaxies at $z=0$ have
experienced SFR concentrations comparable to those of the breakBRDs in their
past. Additionally, the breakBRD state is short-lived, lasting a few hundred
Myr up to ${\sim}2$ Gyr. The observed breakBRD galaxies may therefore be a
unique sample of outside-in quenching galaxies.
