About remainders in compactifications of paratopological groups

In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel«{o} f and meager or Baire. Furthermore, we give a negative answer to a question posed in [D. Basile and A. Bella, About remainders in compactifications of homogeneous spaces, Comment. Math. Univ. Carolin. 50 (2009), no. 4, 607–613]. Some questions about remainders in compactifications of paratopological groups are posed.