@alonerone, more specifically, what “Pub. status: Completed” means is that the original publication came to completion.
Indeed, even when a chapter is marked “End”, that doesn't necessarily mean that the translation into the corresponding language is complete. Sometimes there is a follow-up instalment (and sometimes intermediate chapters are not yet translated).
If a work is truly popular then, even when the original series has ended, the characters may come back. Consider
Kase-san and…, which was completed with five volumes but is now followed by
Yamada and Kase-san.
Of course, you can help to keep creators and publishers motivated to produce characters of the sort that you like; buy either the original series or the licensed translations (when they appear) that contain such characters.