  One of the most dramatic events in the life of a low-mass star is the He
flash, which takes place at the tip of the RGB and is followed by a series of
secondary flashes before the star settles on the zero-age HB (ZAHB). Yet, no
stars have ever been positively identified in this key phase in the life of a
low-mass star (hereafter the "pre-ZAHB" phase). We investigate the possibility
that some pre-ZAHB stars may cross the instability strip (IS), thus becoming
variable. In particular, it has been suggested that some RR Lyrae stars (RRL)
with high period change rates (P-dot) may in fact be pre-ZAHB stars. We present
the first theoretical effort devoted to interpreting some of the high-P-dot
stars as pre-ZAHB pulsators. We constructed a grid of evolutionary tracks using
the Garching Stellar Evolution Code for a chemical composition appropriate to
the case of the globular cluster M3, where a number of stars with high P-dot
values are found. We follow each star's pre-ZAHB evolution in detail, compute
periods and P-dot values for the stars lying inside the IS, and produce
pre-ZAHB Monte Carlo simulations for the case of M3. Our results indicate that
one should expect of order 1 pre-ZAHB star for every 60 or so bona-fide HB
stars in M3. Among the pre-ZAHB stars, ~22% are expected to fall within the IS
boundaries, presenting RRL-like pulsations. On average, the pre-ZAHB pulsators
are expected to have longer periods than the bona-fide HB pulsators, and 76% of
them are predicted to show negative P-dot values. The most likely P-dot value
for the pre-ZAHB variables is ~-0.3 d/Myr, but more extreme P-dot values are
also possible: 38% of the variables are predicted to have P-dot < -0.8 d/Myr.
It appears likely, therefore, that some RRL stars in M3 with high (absolute)
P-dot values are pre-ZAHB pulsators in disguise. (abridged)
