Velez, who is the suspect's girlfriend, was rushed to St. Barnabas Hospital.
She was in very critical condition in intensive care following surgery.
After the alleged stabbing, the suspect climbed out a third-story window and stood on the ledge as he clung to the side of the building.
Police arrived and negotiated with the man for more than 13 hours before he was safely taken into custody.
They set up two airbags to help break the suspect's fall if he plunged to the ground.
Local streets were also closed as authorities tried to talk the man down.
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