How many thousand's of an inch do you let your brass go undersize before you stop loading it?(under the minimum case length)

Most brass stretches when fired and then re-sized, and has to be trimmed back (shortened.) I apologize I do n ot understand what you ask.

The only time I've had brass get shorter is when expanding the neck a bunch. They grow back when shot.

All brass will shorten when fired the first time as it expands to fill the chamber but high pressure can make it flow forward too and lengthen it. Setting it back with dies makes it stretch again the next firing until it needs trimmed.
Straight wall cases always shorten and might never reach max length. All that needs done is to make them all the same length and to check now and then to make sure none stretch over max length. I have .44 brass that has been fired over 40X with heavy loads and none have need trimmed since I evened out the new brass.
They WILL NOT CONTINUE TO SHORTEN, it is a one time thing. But they can get longer.
Revolver brass will shorten, then get longer when sized, then shorten again when fired and never seems to get out of hand, just going back and forth. They might need trimmed so checking is always in order.
Bottle neck cases have to be watched if over worked and trimmed often because cases can fail above the web but this is all due to brass flowing forward from pressure and then sizing full length. They sure will never shorten with use.
I do not know of any cases that keep getting shorter as shot.

I have found brass that after resizing it does not meet the minimum case length. I have also bought brand new Hornady brass and after running it through the resizing die it still was short.This is what I mean; after running it thru the resizing die and it doesn't get any longer, what is the most you will let brass go undersize before you stop using it?

Also, when trimming the 454 brass, it's supposed to be 1.373. Why does some reloading data say to triim it longer than 1.373(ex. Hodgdon loading data from their website says to trim the brass to 1.380) I do not understand this?

The resizing die won't lengthen the brass, shooting it may. Just trim to a consistant length, be it 1.373 or 1.370 or 1.365 and set to seat to the cannelure and load 'em up. Don't push max if considerably under min length, but you should be fine. What's the shortest of your shorts?

CORRECT. Don't worry about only seven one-thousandths of an inch TOO SHORT. Consider it similar to shooting a .38 Special in a .357 cylinder; a .44 Special in a .44 mag cylinder; a .480 Ruger in a .475 Linebaugh cylinder, etc.

DO WORRY about a case that is OVER MAX recommended length. When fired, the case crimp unfolds and lengthens the case and if longer than the chamber, it essentially crimps down the diameter of the throat. As the bullet leaves the case it gets squashed down by the thickness of the brass case wall, creating instantly higher pressures.

We see pics of blown up cylinders and always attribute it to over-loads. Could some be simply due to that "over-length case, esp. if the load is aleady at max?

Just my theory.

I load for the 454 well. Recommended case length is 1.383 with a max of 1.385.

Others gave you good info. It is just not important until brass gets too long for the chamber. It will NEVER get shorter so just make them all the same length for an even crimp. It is rare to buy new brass that even gets near trim length.
It is a non-issue and nothing to worry about.
I have a .44 boolit that will not cycle through a Marlin so I trimmed the brass shorter and it shoots as good as the rifle will allow.