On the Notice of 3-day Pay or Quit, include everything.On the filing for Unlawful Detainer, I file only the Past Due Rents - - but don't expect to collect. 

If he/she does not move out within the given time period, you can serve him/her with a Complaint for Unlawful Detainer.  

Post a pay or quit notice and file unlawful detainer if they do not pay or vacate

If they do not pay within 5 days, then you can file a lawsuit for unlawful detainer.

When the unlawful detainer was served to the tenants, they responded back to the court saying that the unit had habitability issues.

Unlawful Detainer filed through lawyer.December 1: no rent paidDecember 16: Unlawful detainer trial.  

Provided the landlord has given written notice to the tenant that the rent will be accepted with reservation, the landlord may accept full or partial payment of all rent and receive an order of possession from a court of competent jurisdiction pursuant to an unlawful detainer action filed under Chapter 13 (§ 8.01-374 et seq.) of Title 8.01 and proceed with eviction under § 55-248.38:2.

The court actually issues the garnishment,"That means you need a court judgment -- Unlawful detainer or Small Claims -- to file for the garnishment as a motion.Yeah, our balance due can be significant and we really want/need the funds, but don't be surprised that you get zippo from that attempt. 

Provided the landlord has given written notice to the tenant that the rent will be accepted with reservation, the landlord may accept full or partial payment of all rent and receive an order of possession from a court of competent jurisdiction pursuant to an unlawful detainer action filed under Article 13 (§ 8.01-124 et seq.) of Chapter 3 of Title 8.01 and proceed with eviction under § 55-248.38:2. 

I understand the lawsuit must stop if the tenant pays everything that's listed on the unlawful detainer summons, but what if a new month begins before the court date?