Also, the only piece I typically ever replace on my 2004 400 is part number 12+13 about every 2-3 years depending on riding and proper storage (usually causes fuel to start leaking out of the carb uncontrollably).
I've replaced the main spring #3 but after 18 years and 8500+ miles and a clip mod (cutting rings off) the spring tension started to soften and not give smooth transition.
I'm currently looking at replacing the vacuum piston #4 because I'm seeing enough wear on the bottoms it's starting to look machined (as mentioned, LOTS of miles, LOTS of throttle cycles on that slide)
With a bit more information on what is happening before/after the stall I can potentially offer some assistance from experience.
Sometimes these machines will just stall at an idle, being carbureted and such, things like air temp, fuel quality, throttle action prior to slowing to an idle, or just the idle screw setting can make them a bit finnicky. Once you get it to a happy place it will be good for 90% of usage.
Purchase a decent quality in line plastic fuel filter for your machine and install it somewhere in the fuel line before the carburetor, Avoid cheap "screen" filters and look for one with a "paper" element, something the size of a grain of pepper in your carburetor can bring your ride to a sudden and frustrating halt.
If you start doing mods, jet changes, and riding anywhere between -20C and +40C you will need to start playing with carb more often and doing fine tuning.