  The progenitor systems for type Ia supernovae are still controversial. One of
the methods to test the proposed scenario for the progenitor systems is to
identify companions that are supposed to survive according to the so-called
single degenerate scenario. These companions might be affected by supernova
ejecta. We present several numerical simulations of surviving red-giant
companions whose envelopes were stripped and heated. We find that red-giants
with less-massive helium cores ($\lesssim0.30\,M_{\odot}$) can be so faint
after the supernovae that we cannot detect them. In addition, we apply the
results to the case of SNR 0509-67.5, and put constraints on the helium core
mass, envelope stripping, and energy injection under the single degenerate
scenario for type Ia supernovae.
