Those aren't part of the heater core and are just connected to it (see the hose clamps by the fire wall?) They are known to break. It appears you have a different setup from mine- maybe you have rear AC/heat? Worst case you have to replace the lines in the engine bay. (I don't have rear AC so my setup is on the right, and a little easier to replace- I have everything in that right diagram to swap out on mine.)

This link is for reference only- I don't have any experience with this specific part or vendor.

Amazon.com: Heater Hose Line Tube Assembly Front (Inlet & Outlet) With Blend Valve 92408-ZL90B For 2005 2006 2007 2008 2009 2010 2011 2012 Nissan Pathfinder 4.0L V6 5.6L V8 GAS DOHC : Automotive

Buy Heater Hose Line Tube Assembly Front (Inlet & Outlet) With Blend Valve 92408-ZL90B For 2005 2006 2007 2008 2009 2010 2011 2012 Nissan Pathfinder 4.0L V6 5.6L V8 GAS DOHC: Heater - Amazon.com ✓ FREE DELIVERY possible on eligible purchases

www.amazon.com

 

Amazon.com: Dorman 626-688 Engine Heater Hose Assembly Compatible with Select Nissan Models (OE FIX) : Automotive

Buy Dorman 626-688 Engine Heater Hose Assembly Compatible with Select Nissan Models (OE FIX): Heater - Amazon.com ✓ FREE DELIVERY possible on eligible purchases

www.amazon.com

put this one in my 2011 and it works great...takes a little patience to get it between back of engine and firewall but it's not complicated

 

You were spot on! I just bought that pre-fabricated part for $80 and swapped it out. Hardest part was aligning the hoses but that wasn’t too difficult.