If you do not get rust after cleaning with soap, dishsoap, etc it is because you did a very good job of rinsing off the soap.
Soap contains salt, sodium chloride, and is just acidic enough to be corrosive. Residue from dishwasher soap, especially the stuff with lemon, if not well rinsed can deeply pit your stainlessware left in for several days.
This is heresy, of course, we all know soap is lard cooked with lye, how can it rust steel?
Gramma doesn't make your soap anymore.
Modern Soap Producers add salt to their product because salt makes it flow better, that is, easier to pump through the piping system in the plant. I suppose it is a bad analogy but salt also makes your garden slugs flow nicely. . .
Just a few decades ago soap was OK around steel. Then things changed.
Before anyone cared about algae blooms in lakes & ponds the soapmakers neutralized the excess lye in the product by adding just a little phosphoric acid. The phosphorus made great fertilizer for the algae in lakes, not nice for the fish.
A little phosphoric acid also inhibits the rusting process in steel. One example is the "phosphatizing" treatment used on contemporary military weapons.
Along came them dang environmentalists. So to clean up the waterways phosphorus was prohibited in soap. The soapmakers switched to hydrochloric (like, muriatic) acid to neutralize the lye. They still kept the salt, for processing reasons (remember the garden slug). Now there is no more phos acid to inhibit corrosion from the salt. Instead there is just a trace of hydrochloric acid. Hydrochloric is very corrosive = eats the $#*! out of steel.
The wonderful lemon additions to various soaps are also acidic. There are those who might say that leaving lemon dishsoap set in your stainless sink for a week or two will do very unpleasant things, like pit it all the way through.
My education in all this came from:
1. Stainless research at Allegheny Ludlum
2. At Rolled Alloys, years of providing technical support for stainless & nickel alloy applications at chemical process customers.
3. Private conversations w metallurgists at a very large midwestern soap manufacturer
4. Watching the after-rust in my barrels rinsed w hot water & some kind of soap.
Grampa never shot a breechloader til he was 18. Told me he used Cold Water to clean his rifle. Grampa knew his stuff.
Me, I'd keep soap, ammonia and hydrogen peroxide, all of them, out of my barrel. Cold water does wash out black powder residue. Hot water rusts things faster than does cold. I suppose that a further addition, soap anyway, may be needed to clean out patch grease. Do rinse out the soap with cold water. Then dry & oil with your favorite hopefully water-displacing oil
Jim Kelly, Heretical but Humble Metallurgist