Air check valve question

After the smog pump, there's the air check valve. One line goes to the back of the cylinder head and the other down below the car. I assume that went to the catlytic converters or something. My car has no cats but does have long tube headers, etc. Currently the line heading down below the car is in pretty bad shape and just venting to the atmosphere (making a lot of puffing noises). Should this line be capped or left to breath?

Sorry, this is probably easy. I tried to search for the answer.

Thanks!

Thanks Hissin. I just got the car and that's the way it was set up. I've been told that it's difficult to cap the cylinder head and it can make the car run poorly. True? I've seen the smog pump delete kits, is this a hard install?

Thanks again for the reply.