I bought this truck 3 years ago and after about a year I found out that it doesn't have a cat converter. The truck is from South Carolina but purchased in North Carolina. I don't know the laws there. Since I'm and old guy, 82, in Georgia, the law is, if I drive under 5,000 per year and am older than dirt, I don't have to have an emissions inspection. I don't know what else it may be missing. I don't know how it runs without an O2 sensor and a converter.
Where would the converter be located normally?
Where would the O2 sensor normally be?

It's a 4.6L engine 2002 XLT F150.
I've considered selling it but any buyer in Ga wouldn't be able to drive it.

 

Pictures from the interwebs suggest there are two of them right before the Y into a single exhaust.

 

There was a time when tuners would turn off the 02's to prevent throwing codes..
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The diagram in post #3 is generic and your 4.6 does not have the devices (pre-converter?) located upstream of the large catalytic converters. Your engine, 4.6 liter, has two catalytic converters as depicted and these tie into a single exhaust pipe that goes to the muffler located further back and not shown. The upstream Oxygen sensors are located in the downcomer pipe just past the flanged connection to the exhaust manifold. The downstream Oxygen sensors are located in the side of the catalytic converters. Your engine has two exhaust manifolds thus two (2) upstream Oxygen sensors and two (2) downstream Oxygen sensors.
Catalytic converters get removed for all sorts of reasons, theft, perceived poor performance, clogging etc.
Removing the catalytic converts causes a Check Engine light to be illuminated on your trucks instrument panel and this by itself will cause you to fail emissions testing.

G Rich,
A couple of questions for you.
Is your Check Engine Light illuminated?
What causes you to believe your catalytic converters have been removed? Most of the time persons "rod out" (remove the internals but leave the shell of the catalytic converters) vs actually remove them. This will cause a check engine light unless your truck's computer is reprogramed (unlikely) to ignore the Oxygen sensors.

My little story- I recently sold a 1998 Lincoln Town Car to an individual who lives a couple of miles away. Car was running fine with no codes. Two days later she calls me and says it won't start so I drove over there to see what's up. Lifted the hood and half of the electrical connectors were apart, I reconnected them and the car started right up. A few days later she call and says the check engine light is on. I drove over a said what's been touched and she replied the catalytic converters had been rodded out to improve performance. I have not been back and I suspect that car is no longer operating. It is a shame since it was a very good car. BTW an intact catalytic converter can be recycled for about $200 each a rodded out cat is worthless

 

Not having emissions is fine, but most folks do hack repairs like you mention, OP, to get around more expensive work that’s needed.

Engine misfires nonstop and roasts the converters? Heck, we’ll hack them off and fleet on with life. Ooga booga! Converters expensive, straight pipe not!

 

If the truck has no cats, you can smell it !!
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It has been a long time since I have had cats installed, but a local exhaust shop should have a generic cat they can throw on for pretty cheap, relative to the cost of performance or oem parts anyway.

As for O2 sensors, there should be a bung before and a bung after the cats, one for upstream sensor and one for downstream sensor.

 

It has been a long time since I have crawled under an early 2000s F150, but according to the ford parts diagram, his exhaust should look exacatly like what is depicted in the image in the post from David Hineline

https://ford.oempartsonline.com/v-20...ust-components

 

Technically its a violation of ann Un-Constitution Federal Law to remove emissions equipment

 

Seems to me like the OP does not really care about his post.