The state or condition of living together, especially as unmarried partners; shared habitation.
From cohabit plus the noun-forming suffix -ancy. This creates an abstract noun describing the state of cohabiting.
This word became important in law and sociology when people started studying unmarried couples—it's the noun you'd use if you're discussing whether cohabitancy affects taxes or legal rights.
Complete word intelligence in one call. Free tier — 50 lookups/day.