  Type Ia supernovae (SNe Ia) play important roles in our study of the
expansion and acceleration of the Universe, but because we do not know the
exact nature or natures of the progenitors, there is a systematic uncertainty
that must be resolved if SNe Ia are to become more precise cosmic probes. No
progenitor system has ever been identified either in the pre- or post-explosion
images of a Ia event. There have been recent claims for and against the
detection of ex-companion stars in several SNe Ia remnants. These studies,
however, usually ignore the angular momentum gain of the progenitor WD, which
leads to a spin-up phase and a subsequent spin-down phase before explosion. For
spin-down timescales greater than 10^5 years, the donor star could be too dim
to detect by the time of explosion. Here we revisit the current limits on
ex-companion stars to SNR 0509-67.5, a 400 year old remnant in the Large
Magellanic Cloud (LMC). If the effects of possible angular momentum gain on the
WD are included, a wide range of single-degenerate progenitor models are
allowed for this remnant. We demonstrate that the current absence of evidence
for ex-companion stars in this remnant, as well as other SNe Ia remnants, does
not necessarily provide the evidence of absence for ex-companions. We discuss
potential ways to identify such ex-companion stars through deep imaging
observations.
