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Hi all, hopefully someone can straighten my thoughts out for me. I have a Poulan/Husqvarna lawn tractor with a Briggs 40N877-0004, at the beginning of season changed the oil, spark plugs, battery, and filters. Since then it's been running top notch up until I went to start it today.

Today I tried cranking it and it wouldn't even crank, battery is not the issue, it was like it had too much compression. Then noticed fuel was dumping out of the exhaust, too much compression for sure now!

Filled the fuel tank yesterday in hopes of cutting the grass but got rained out, today the tank is completely empty. First thought on a smaller engine would be needle valve or stuck float, but this engine has the mechanical fuel pump. Wouldn't it be required that the engine is running, or at least cranking, for the fuel to continuously feed into the cylinder before leaking by and dumping out the exhaust?

Check for gas in oil, remove spark plugs & crank engine, install fuel shutoff valve before fuel pump, reinstall plugs & give it a try.

sounds like your float needle in the carburetor has failed. At the minimum you'll need a new needle. You can also pull the vacuum line off of the fuel pump and see if any fuel is in it, as well to be sure there isn't a hole in the diapgrahm of the pump. If it has the pump im thinking of, it is not repairable. just a new pump is needed.
buy a couple quarts of cheap oil, enough to do 2 changes or so, and filters. drain the oil, refill it, run it for awhile (10-15 minutes), drain it, (careful, itll be hot). new filter and new oil, run it, drain it. and on this change use your favorite oil and filter.

I understand how to fix the problem, the question is...

"...Wouldn't it be required that the engine is running, or at least cranking, for the fuel to continuously feed into the cylinder before leaking by and dumping out the exhaust?"

No it will happily syphon out while the engine is off
When running the engine will flood a bit which will bring the engine back to normal operating conditions from before the brain dead EPA started making regulations that do nothing for pollution abatement but it keeps them in a job.

I've seen some that have a high fuel tank and still have a fuel pump. When gravity for that particular mower would do fine.