  Core-collapse supernovae (SNe) of Types Ib and Ic arise from
hydrogen-stripped stars, while the latter are also stripped of their helium.
Both SN types have a similar temporal evolution, suggesting broadly similar
progenitors. However, while some Ic SNe are associated with relativistic jets
of gamma-ray bursts (GRBs), no GRB has yet been found in association with Type
Ib SNe. Here we find that, even if GRB-like central engines operate in both SNe
Ib and Ic, different properties of their envelopes may accommodate this
potential tension. In particular, we focus on the case of a low-mass, extended
envelope surrounding the progenitor star (as produced, for example, by strong
mass losses prior to explosion). If the envelopes of Type Ib SNe are
sufficiently massive ($M_{\rm ext}\sim(0.3-1)M_\odot$) and extended ($R_{\rm
ext}\sim 10^{13}\text{ cm}$), we show that (i) GRB-like jets cannot break out
of the star; (ii) the SN light curve is compatible with current observations.
Different envelope properties of Type Ib SNe with respect to (at least some)
Type Ic SNe may be connected to the presence of a helium layer surrounding the
star.
