Do weak acids have strong conjugate bases?

Flexi Says:
Weak acids, like strong acids, ionize to yield the H+ ion and a conjugate base. Because HCl is a strong acid, its conjugate base (Cl−) is extremely weak. The chloride ion is incapable of accepting the H+ ion and becoming HCl again. In general, the stronger the acid, the weaker its conjugate base. Likewise, the weaker the acid, the stronger its conjugate base.