Okay so this isn't a <em>really</em> common phrase, but I'll do my best to use it in a sentence for ya. "Everyday on end there are 500 kids in my grade." I'm pretty sure this makes sense, if not heres a definition of the phrase "on end": "On end" means "without a break", which has been changed over time so that "days on end" now often means "several days"
The old woman meant she is taking charge of her own children and grandchildren. Meaning if she is gone non of her children nor grandchildren will be able to support themselves. If she is alive is for a reason. By helping her own family needs.