My brother rents his condo to someone in section 8. June 1st section 8 terminated the lease for not making repairs. The repairs were started in Aug. and the bathroom had to be gutted. The water had been turned off because the renter had not paid the bill. The renter was told the repairs would take 3 days, and they would have to leave for the 3 days. It is now the middle of September, and the tenant has yet to leave. Rent has not been paid to my brother since May 1st. How can the tenant be removed without filing an eviction notice. Isn't this considered as squatters? How can someone live in a condo without running water? Help! This is in the state of NJ.

No they are not squatters. In fact there really is no such thing any longer.

They were the legal renters, that just refused to move, and have been living rent free. There is no way to remove them without filing eviction. Why would they not, and why have they waited so long to do so?

Landlords file evictions all the time, it is just part of being a landlord.

... How can the tenant be removed without filing an eviction notice [?] ...

You don't "file" an eviction notice. You simply hand them something in writing in which you demand that they be out in the required time, or you will ask a judge to order a peace officer to remove them. In other words, you will sue them for eviction.