  Massive stars with a core-halo structure are interesting objects for stellar
physics and hydrodynamics. Using simulations for stellar evolution, radiation
hydrodynamics, and radiative transfer, we study the explosion of stars with an
extended and tenuous envelope (i.e., stars in which 95% of the mass is
contained within 10% of the surface radius or less). We consider both H-rich
supergiant and He-giant progenitors resulting from close-binary evolution and
dying with a final mass of 2.8-5Msun. An extended envelope causes the supernova
(SN) shock to brake and a reverse shock to form, sweeping core material into a
dense shell. The shock deposited energy, which suffers little degradation from
expansion, is trapped in ejecta layers of moderate optical depth, thereby
enhancing the SN luminosity at early times. With the delayed 56Ni heating, we
find that the resulting optical and near-IR light curves all exhibit a
double-peak morphology. We show how an extended progenitor can explain the blue
and featureless optical spectra of some Type IIb and Ib SNe. The dense shell
formed by the reverse shock leads to line profiles with a smaller and
near-constant width. This ejecta property can explain the statistically
narrower profiles of Type IIb compared to Type Ib SNe, as well as the peculiar
Halpha profile seen in SN1993J. At early times, our He-giant star explosion
model shows a high luminosity, a blue color, and featureless spectra
reminiscent of the Type Ib SN2008D, suggesting a low-mass progenitor.
