TWO STARTERS GOT BROKEN I GUESS FROM THE FLYWHEEL. IS THAT POSSIBLE

I Edited your post to make some sense.
The starter fails. hard and makes only huge sound engaged.
battery ok.
seen that many a time me working long ago on cars fixed by farmers, etc, lacking good or correct parts.
first learn rule #1 the starter pinions are not all the same size
seems it is 9 tooth
or are the whole starters. , so what you have is a wrong starter and or wrong flywheel.(or both are wrong, omg don't be there)

the parts must be for the 4.9L ford engine only! 9tooth.
not only that but there are 2 flywheels just for this engine not counting not told is car with A/T or M/T .(I guess stick shift?)_
10" fly and 11", used. Teeth: 164; Outer Diameter: 10"
I well show starters now, delco 4.9L ONLY
ACDELCO 3371057 Gold , for auto trans only(high power)
ACDELCO 3361033 Gold , M/T.

the A/t starter fits but has more KW power to run that power wasting A;/t transmission, the transmission pump spins with starter'.

all those parts must match and you did not do that.

and fire your autostore guy, .

the ford site this shows all starters used here.
slows this.
9-Tooth Pinion 1983 to 1991 is the year range.
oem orig.
3180n https://www.obbstartersandalternators.com/all-c-0.html?part=Starter&make_id=Ford&model_id=Truck&submodel_id=F-150&part_year=1987&part_engine=6+Cyl.+4.9L+300cid

all this for one word BING (the sound of jammed jammed up starter.
there sure are other causes.

If the starter is running but not turning the engine, then there are a few possible issues.

1. Starter gear teeth are stripped.
2. Flywheel has broken tooth/teeth
3. Starter-to-flywheel mounting out of adjustment and needs shimmed.

possible broken ring gear on flywheel

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Sounds like the teeth on the flywheel ring gear are damaged.

There are a few possibilities and I will relate to other Brands as I have not worked on a Daewoo.

In some cases, the starter and flywheel are trying to crank a Locked-up engine. Sometimes with electric cam timing and crank position sensing, the controls get out of Sync. There is compression when there should not be. It is also possible to get something similar to a hydraulic Lock-up caused by a leaking fuel injectors spilling into the cylinders.

To test for that would generally be to put a pressure gauge on the fuel test port and see if the fuel pressure dropped overnight. This would indicate leaking injectors which are flooding your engine. This problem would constantly break your starter and flywheel.

I would also recommend buying starters with "lifetime" replacement warrantees so you eliminate the expense of replacement starters.

Some Brands of cars require "SHIMS" in mounting the starter to the engine or bellhousing. This helps with meshing the teeth of the flywheel and starter.

BE SURE that the number of teeth on the starter drive is correct. Some Brands have say 12 teeth and for sake of discussion 14 teeth. These teeth are cut from the same size block of metal. Obviously 12 teeth are bigger than 14 teeth occupying the same space. But if the flywheel is matched for 12 teeth any other pattern will not mesh. You will have a coarse tooth trying to fit the space of a fine tooth. Something is going to grind itself smooth and then fail.

I hope my solution will help you. Along the lines of Engine controls you might consider your engine is overadvanced. Typical engines start in a "cold start" cycle and then advance to lean the fuel mix. Sometimes the heat sensors which reset the spark advance do not work and keep the engine overadvanced. Being overadvanced will increase compression and make the starter strain. The temperature sensors are inexpensive and might be a good guess for a replacement part.

You can't shim Ford starters. First check to make sure you're getting correct starter... Ford 6's have a couple different "noses"/inputs - some actually extend further in. So check to make sure you're getting the correct part from your source. If it is correct part, you're going to have to replace flywheel. Also before putting in starter, check the flywheel for "burrs" - tiny metal particles left behind from old starter on flywheel. Almost like metal shavings between teeth of flywheel.

Remove the starter shields and check the starter drive. Does it fly out when the starter is engaged? Check the flywheel for ring gear damage from the starter. Check the flywheel for breakage at the crankshaft, try to turn the engine using the flywheel with a screw driver.

I would check current draw with a good ammeter & se how much current the starter draws when cranking. I owuld guess about 400 amps, but check with Delco. Other possibility is starter is binding on flywheel.
Did you disassemble one of the faulty staters to see if armature is rubbing on magents or coils?
Are these starters remans or new? Remans sometimes have problems.

What do you mean by shattered? If you mean the teeth on the starter motor, you are probably looking at a problem with broken teeth on the flywheel on the engine. Inspect it for damage. MM85