little hose identification

[dav34]

Hello to all Volvo fans,

My wife owns a 2003 Volvo S80 2.4 liters petrol, with manual gearbox.
I'm involved in oil changes and small repairs (brakes, filters...).
Today, I noticed a small hose that goes from the air box to the top of the motor, which was disconnected. I tried to connect it back, but the connection part is completely destroyed (see pics, both sides of this very tiny hose in yellow, and the connector).

IMG_2756.jpg (32.61 KiB) Viewed 649 times

I have 2 main questions, and I really can't find any resources for this, that's why I'm asking your help :
- What is the function of this small hose ? what is the risk if not connected ?
- Do any of you has access to Volvo parts numbers, to tell me the exact part number to search for a new one ?

Thanks in advance,
David.

[dav34]

For future readers, it seems that the "connector" is available separately, part reference : 1332455.
I wish a nice day and a good repair for any future reader.
Be safe, good ride.