Hi neesaki, remember all this took place in a 2 minute timespan. He was bleeding out and going hypovolemic once the vena cava was sliced. We don't exactly when she stabbed the chest, it seems like it occurred at the sink in the bathroom. The defensive wounds probably took place from the shower and run to the sink, a matter of seconds.
Also, being alive can have many definitions. It could mean brain activity, a cardiac rhythm without pump action, we just don't know because none of us were there, we can only surmise. It is considered life as long as there is brain activity and a heartbeat. Brain activity doesn't necessarily mean consciousness.
From my experience, hypovolemic shock will cause supraventricular tachycardia and as the blood volume is not replaced, the heart will either go into a ventricular fibrillation or cardiac standstill. Either of those will not have pump action. The normal fight or flight response was most likely taking place as he tried to escape, but this adrenaline rush increased the vena cava spill as his heart raced I am sure to over 200 beats per minute.
Oh dear, I don't want make this sound gory to non medical personnel, I just hope I am making sense. He would still have life in his body after he was down on the floor, but not the kind of life you or I have with not being wounded. The last cut, slitting the jugular would still cause oozing of venous blood, as the coagulation would still be normal. If he was in cardiac standstill, the carotid would not pump. Travis was a young healthy man and all of his arteries, veins, heart muscle were in excellent shape, so they would have fought like heck to keep the body alive, it is called homeostasis and I am sure this was occurring but it was a futile fight. He could not have been conscious when this all started after that fatal knife stick and he became hypovolemic. I have never seen anybody in shock like that remain conscious, alive yes, conscious no.
That was a good question and made me think. If I wasn't 70 years old and so arthritic, I would still love to be working in my beloved nursing!!