Documentation: Face used to indicate that a headline is DONE. This
face is only used if `org-fontify-done-headline' is set. If applies
to the part of the headline after the DONE keyword.
IOW you have to set org-fontify-done-headline to nil.
Following @lawlist advise, using :box attribute for mode-line-inactive made it.
The mode lines images shown in the question are from inactive frames.
The second image shows an inactive frame with a mode line that does not render the straight lines.
(set-face-attribute 'mode-line-inactive nil :box t)
renders the straight line with foreground color: