Depending on the state, Verizon will terminate the DS1 at the Rate Demarcation Point (DRP) stipulated in their state tariff.

In New York, the DRP is within twelve inches of the the customers premises. Know what Vz installers in New York City do, the tech will wire extend a DS1 delivered on fiber using house cable or what ever is available. Typically using HDSL2, since one pair is easier than two.

I once was a Field Manager in NY, so I know the typical tech's approach.

If the location can only be fed on copper cable, then the tech will push the circuit up on available copper pairs. Hopefully HDSL2 from the CO or a CEV.

The only potential problem is that if the HDSL span from the CO requires a doubler (Repeater) unit, Vz OSP will engineer the HDSL span as four wires since there are no approved HDSL2 doublers in Vz.

By the way. The HTU-R HDSL remote is a defacto T1 NIU (Smart Jack), since the HTU-R hands off the DS1 at the mountings built in RJ-48C interface.