  The interplay of charge orders with superconductivity in underdoped cuprates
at high magnetic fields ($H$) is an open question, and even the value of the
upper critical field ($H_{c2}$), a measure of the strength of
superconductivity, has been the subject of a long-term debate. We combined
three complementary transport techniques on underdoped
La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4}$ with a "striped" charge order and a low
$H=0$ transition temperature $T_{c}^{0}$, to establish the $T-H$ phase diagram
and reveal the ground states in CuO$_2$ planes: a superconductor, a wide regime
of superconducting phase fluctuations (i.e. a vortex liquid), and a high-field
normal state. The relatively high $H_{c2}$ is consistent with the opening of a
superconducting gap above $T_{c}^{0}$, but only at $T\sim (2$-$3)T_{c}^{0}$, an
order of magnitude below the pseudogap temperature. Within the vortex liquid,
an unanticipated, insulatinglike region, but with strong superconducting
correlations, begins to emerge already at $T\lesssim T_{c}^{0}$. The results
suggest that the presence of stripes plays a crucial role in the freezing of
Cooper pairs in this novel state. Our findings provide a fresh perspective on
the pairing strength in underdoped cuprates, and introduce a new avenue for
exploring the interplay of various orders.
