I know that falloir has only one subject case that is 3rd-person singular (il) and it's only valid to say il faut and il fallait. An object can also be supplied like il me faut and il nous faut.
But is it grammatically correct to say on me faut or on m'a fallu? They sound OK to me. Does this apply to other il-only verbs like pleuvoir or s'agir?