  We develop a global wellposedness theory for weak solutions to the 1D
Euler-alignment system with measure-valued density, bounded velocity, and
locally integrable communication protocol. A satisfactory understanding of the
low-regularity theory is an issue of pressing interest, as smooth solutions may
lose regularity in finite time. However, no such theory currently exists except
for a very special class of alignment interactions. We show that the dynamics
of the 1D Euler-alignment system can be effectively described by a nonlocal
scalar balance law, the entropy conditions of which serves as an entropic
selection principle that determines a unique weak solution of the
Euler-alignment system. Moreover, the distinguished weak solution of the system
can be approximated by the sticky particle Cucker--Smale dynamics. Our approach
is inspired by the work of Brenier and Grenier [SIAM J. Numer. Anal,
35(6):2317-2328, 1998] on the pressureless Euler equations.
