Partial fills: what does your strategy actually do?

Genuine question rather than a lesson, because I suspect my answer is wrong. I send an order for a hundred shares. Sixty fill, forty rest. My strategy was written as though orders fill completely or not at all, and I've never explicitly decided what should happen in between. Options I can see: wait for the rest, cancel the remainder and proceed with sixty, or cancel and treat the whole thing as not having happened. Each implies something different about my exit logic — a stop sized for a hundred shares is wrong for sixty in a way that matters. What do people actually do here? And more importantly, did you decide it deliberately or did you find out what your code does by watching it?