It is rare that a tenant/occupant will vacate after receiving an eviction notice, but proper notice is required by law. Some tenants/occupants vacate after the eviction notice expires, but before the trial date. Most will not vacate until after the eviction trial.
If your tenant vacates after receiving the eviction notice, but before the eviction lawsuit is filed, then an eviction lawsuit should not be filed (the court cannot evict a person who has already vacated the property).
On the other hand, if the tenant vacates after the eviction suit is filed (and the tenant/occupant has been served by the Constable), then you are entitled to continue the case to obtain a judgment for the unpaid rent and court costs.