  We study the structure and stability of spherically symmetric Brans-Dicke
black-hole type solutions with an infinite horizon area and zero Hawking
temperature, existing for negative values of the coupling constant $\omega$.
These solutions split into two classes, depending on finite (B1) or infinite
(B2) proper time needed for an infalling particle to reach the horizon. Class
B1 metrics can be extended through the horizon only for discrete values of mass
and scalar charge, depending on two integers m and n. For even m-n, the
space-time is globally regular; for odd m, the metric changes its signature on
the horizon but remains Lorentzian. Geodesics are smoothly continued across the
horizon, but for odd m timelike geodesics become spacelike and vice versa.
Causality problems, arising in some cases, are discussed. Tidal forces are
shown to grow infinitely near type B1 horizons. All vacuum static, spherically
symmetric solutions of the Brans-Dicke theory with $\omega<-3/2$ are found to
be linearly stable against spherical perturbations. This result extends to the
generic case of the Bergmann-Wagoner class of scalar-tensor theories with the
coupling function $\omega(\phi) < -3/2$.
