  We prove that there exist Banach spaces not containing $\ell_1$, failing the
point of continuity property and satisfying that every semi-normalized basic
sequence has a boundedly complete basic subsequence. This answers in the
negative the problem of the Remark 2 in H. P. Rosenthal. "Boundedly complete
weak-Cauchy sequences in Banach spaces with PCP." J. Funct. Anal. 253 (2007)
772-781.
