  This work studies relativistic stars in beyond Horndeski scalar-tensor
theories that exhibit a breaking of the Vainshtein mechanism inside matter,
focusing on a model based on the quartic beyond Horndeski Lagrangian. We
self-consistently derive the scalar field profile for static spherically
symmetric objects in asymptotically de Sitter space-time and show that the
Vainshtein breaking branch of the solutions is the physical branch thereby
resolving several ambiguities with non-relativistic frameworks. The geometry
outside the star is shown to be exactly Schwarzschild-de Sitter and therefore
the PPN parameter $\beta_{\rm PPN}=1$, confirming that the external screening
works at the post-Newtonian level. The Tolman-Oppenheimer-Volkoff (TOV)
equations are derived and a new lower bound on the Vainshtein breaking
parameter $\Upsilon_1>-4/9$ is found by requiring the existence of static
spherically symmetric stars. Focusing on the unconstrained case where
$\Upsilon_1<0$, we numerically solve the TOV equations for polytropic and
realistic equations of state and find stars with larger radii at fixed mass.
Furthermore, the maximum mass can increase dramatically and stars with masses
in excess of $3M_\odot$ can be found for relatively small values of the
Vainshtein breaking parameter. We re-examine white dwarf stars and show that
post-Newtonian corrections are important in beyond Horndeski theories and
therefore the bounds coming from previous analyses should be revisited.
