Let's see if we can give you some insight about WWII uniform issues...
Uniforms to enlisted personnel are government property and they are issued out in basic training. When a soldier needed a new shirt, tie, trousers, boots, etc., they had to turn the used pieces of clothing in to supply in order for the supply NCO to issue a new piece of clothing.
Uniform pieces in combat were exchanged for clean uniforms at a clothing exchange and bath point. Soldiers would come in to the point, strip naked and take a shower. They would then proceed to a clothing issue point where they would receive replacement uniforms.
Soldiers deploying to a combat zone would have two duffle bags- an "A" bag and a "B" bag. The "A" bag was used to hold important personal and issue items that were of the most importance to a soldier. This is where extra fatigues, all of the soldiers' socks and underwear, and other items that a soldier might need that don't fit into the combat pack go. Items like Dress uniforms like the four pocket that started the thread would have gone in a "B" bag which would have spent a lot of time in storage at the regiment or division level. The only times that the "B" bag would come out was when soldiers were heading back to the rear areas for rest, or refitting.
When a soldier died, was killed, or taken POW, all of the soldier's items would be inventoried by an officer and an NCO (usually). All personal items would be segregated and placed in a bag. All of the issue items would be returned to the supply system, but first, they would be sent to a Quartermaster unit that would launder the items and then evaluate the uniforms for appearance and serviceability. Items with tears, holes, missing buttons etc. would be sent to a renovation point where the clothing would be reworked to make it serviceable for another soldier.
There are a couple of things to remember. In WWII, virtually all clothing was washed in hot water. Even wool items would be laundered. Some clothing would shrink. After the items dried, they would be checked for size accuracy. This is you would will see jackets with a 38R size label and an ink stamp reading a smaller size like 37S. When that happened, the jacket would be reissued under the newly identified size. MOST used clothing would be issued with a "combat serviceable" tag, meaning that it was not supposed to be re-issued as a component of a dress uniform. Another thing done at the clothing reclamation point would be to line through any names, service numbers or even laundry marks, so that there would be no confusion that the new owner might not be the rightful owner of the piece of clothing.
In the case of the jacket that started this thread, the first owner PROBABLY turned the blouse in for a new one PRIOR to leaving the US. I would find it very unusual for a jacket to have traveled to the ETO and then to be shipped back to the Pacific later. There would have been plenty of need for uniforms in the ETO.
Finally, as soldiers were getting out of the military, they would go to separation centers to be processed for discharge. One of the last steps prior to discharge is that all soldiers were issued new clothing IF THEY NEEDED IT> only one dress uniform would have been issued. This is where the jacket was probably issued to the soldier who went home wearing it.
I hope this helps.