The older mowers had a hole in the deck and the muffler was installed from the bottom and exhausted into the grass. Toros used this on some of their quality models.

Maybe the previous owner used one of these engines and mounted it on a different deck and he didn't know where to put the muffler either !!!

Thanks for the info. I do not believe that would work for this engine. If it was a screw- on type of round canister muffler I would drill a hole in the deck and give it a try.
However, it is not. It is the type of opening with a unthreaded access with two threaded holes for the muffler bolts. So.....even if this was a replacement engine it still does not explain the type of muffler that would need to be mounted. I am still baffled by this and am anxiously awaiting a solution or explanation.

Baymee really had given you the best explanation you will get. To get a muffler installed on this, you will need to bore a hole in the deck and install an under deck muffler. Toro had 2 different length mufflers.I don't recall if they were used on steel deck machines. Below is a link to the shorter one. Only you can decide if it is safe to do and within your capabilities. There was also an odd above deck muffler that looked more like a tube on some misc mower if you wish to search. Or , you have yard art....

Here is a link that might be useful: muffler

The deck on the Toro where I saw this muffler was cast and it was the long one. It was held in place with 2 bolts.

Thank you to baymee and tomplum for giving me answers to my muffler problem.
Well.....it looks like I bought a mower from a less than honest seller. LIke that's never happened before!!
I did some further checking and either the engine was swapped for a different one or the mower deck was replaced. I am guessing the engine. It is a Tecumseh ECV100-145315G and NOT a LEV115-360021C as the label for Craftsman cross-referenced to. Big difference!
Anyway, since I do not want a piece of yard art I will attempt the retrofit myself. I have located the correct muffler and will be cutting a hole in the deck. Wish me luck and thanks again!!!

I assume in your original posting that you got the engine # off the owners manual and not the actual engine?

ECV100-145315G = 143.384112
LEV115-360021C = 143.996004

bill_kaupon : Nope.....You assume wrong. I got the numbers off of the tag that is mounted on the mower deck. I guess the previous owner either had a mower deck that rusted away and he removed the muffler from the engine so it would fit on a "replacement "deck. OR the engine went bad and the replacement engine had to have the muffler removed to fit. Either way......wrong engine for the mower deck. Lesson learned: Never trust the labels on the mower.....always check the engine itself! Even though the engine is a Exclusive Craftsman Vertical I was still fooled!

that's the problem buying used. You got to really check them out. IMO I don't believe anything the seller is telling me. I look for the truth in the machine based on my knowledge, inspection technique, and dollar amount I am willing to spend. Muffler's rarely wear out before decks or engines due to neglect... Tec with mufflers on the side of the block made millions so you should be able to find correct engine for the deck about as cheap as new muffler.

I would think that model with the muffler pointing down inside the cutting area is why you don't see many left due to the decks were all rotted out from cracks caused by grass, dirt, moisture, and now hot exhaust. Which would make the engine the only thing that would out last the muffler and deck.