Interesting question, the smallest pistol you'd trust. I'm assuming we're talking about bad guys, probably at relatively close range, and not bears or laser-throwing zombies at distance. Hmmm, personally I definitely would trust a 9 mm., I definitely would not trust a .22, and I probably would not trust a .32. So the "gray area" is somewhere around the .380s and .38s. It's tempting to say that it depends on what you expect to encounter, but the problem is that sometimes you can encounter a little more than you expect. All things considered, I'd probably go as low as a Makarov 9x18 in an area where I didn't expect any problems. The stopping power is, depending on cartridge choices, somewhere between a .380 and a .38 Special, and I could live with that. I hope.
Needless to say, I'd prefer something a little bigger, but that wasn't the question.