If धातु disappears because of अर्धधातु, then गुण and वृद्धि do not occur at the place where that अर्धधातु occurs.
examples:
चिय् + चि + य् = चे + चि + य = चेचिय: (note that the end result is not चिचेय: because the अर्धधातु - अच् at the end if being cut short and hence the गुण and वृद्धि cannot occur at the place. The गुण and वृद्धि occur at the precedent चिय् instead)
Another example is मरी मृज:
मृज् + मृज् + य्
= म + मृज् + अ
= मरीक् + मृज् + अ ( रीगृदुपधस्यच)
रीगृदुपधस्यच is the realization of the rule (न धातुलोप अर्धधातुके) here.