The shtick with the investment scheme is that she is going to claim that the heir ran off with the money, leaving her blameless. The question of whether or not it will be believed remains open., but she's been playing vapid in public forever; lots of men of that time and place might have assumed she was too stupid to have pulled off such a scam. (Also, many of the "Ton" were not well-educated in practical matters, but were often loathe to admit it. It's not beyond the realm of possibility that such people would eat the loss rather than admit to being swindled through their own gullibility and ignorance.) The F family have been, as the saying of the time went, "punting on River Tick" for quite a while, but had rather successfully managed to hide how bad it was and blame that on the heir's negligence. In that era there were a lot more possibilities for money just disappearing -- she could even claim that the ship to America went down, taking the heir AND the gold with it.
BTW, about the Featheringtons: 1: the housekeeper's green dress is livery, a uniform, so of course she's wearing it every time we see her. 2) Penelope's room does have a ridiculous number of candles, but she may be buying them herself. She is presumably staying up late to write when she won't be disturbed, and candles (along with quills & paper) are the tools of her trade. They are also relatively small and easy to hide, so I think it's plausible that she has her own stash of them, especially now that they have presumably cut way down on the number of servants in the house who might notice them and tell. (It's also possible that she might be slipping a bit of extra cash to the housekeeper and claiming that it was saved from when her father was still alive; the housekeeper knows her mother is a spendthrift who thinks Pen is something of a freak, so it's plausible that she might have hidden some cash from Mommy dearest.)