what bike is this?
see if you can trace the metal pipe goes to where?
if it's a Yamaha YCLS system, then it's a return hose for extra 2T when you close throttle

if it's the Y80 with autolube, quite likely it's the oil return hose
I'd suggest removing the broken part, and get a clear oil hose to join to the metal hose, and push the other end of the clear hose into the white oil tank. If needed, make the oil tank hole bigger to fit

ok, then it's similar to Y100, that is just atmospheric or overflow hose

ignore
don't overfill 2T can liao