I have an 88 f250 with a 5.0 engine. (I know it's an f150 forum). The tube coming off the diverter valve that runs down to the exhaust has been cut off (before I owned it) the guy put long tube headers and straight piped it so I have no cats. What will this cause? Will it cause problems in the future? Iv checked all the lines in my thermactor system and they all look good except the one running to the exhaust that has been cut off. I have a code 44 as well. Is that tube being cut off cause that code. There is no check engine light.

 

All that will happen is that when the valve opens to pump fresh air down to the cats it will pump it back into the fresh air because you don't have any cats.
If you ever got an over zealous roadside inspector you might have a bit of a problem, because even if you don't have to take it for an e-test it's against the law to remove any emissions control equipment. They might be a little more upset with the lack of catalytic convertors than the lack of an air pump tube.
Chances of that happening are pretty slim. (but....)