False information spreads on social media, and fact-checking is a potential countermeasure. However, there is a severe shortage of fact-checkers; an efficient way to scale fact-checking is desperately needed, especially in pandemics like COVID-19. In this study, we focus on spontaneous debunking by social media users, which has been missed in existing research despite its indicated usefulness for fact-checking and countering false information. Specifically, we characterize the tweets with false information, or fake tweets, that tend to be debunked and Twitter users who often debunk fake tweets. For this analysis, we create a comprehensive dataset of responses to fake tweets, annotate a subset of them, and build a classification model for detecting debunking behaviors. We find that most fake tweets are left undebunked, spontaneous debunking is slower than other forms of responses, and spontaneous debunking exhibits partisanship in political topics. These results provide actionable insights into utilizing spontaneous debunking to scale conventional fact-checking, thereby supplementing existing research from a new perspective.