It's theoretically possible for Mom to survive the first chapter, but only if Wendy gets unjustly cheated out of her savings or that thaumacard gets stolen. I'm guessing it's not going to be that, though, if only because I think this comic is going to be more "Fantasy Action" than "Fantasy Tragic Cycle of Poverty."
Seriously, though: If you're saving up for some big, important investment at the start of the story, you're going to either get all your hard work destroyed at the last second or wind up losing the very thing you hoped your investment would help. Those are literally the only two options.