What is the ruling regarding someone who vowed a sum of money, then invested it and lost it, and is his vow considered valid, and what should he do if he finds it?

You are not sinful for your vow, because a vow is valid with money that cannot be delivered, such as usurped money. The validity of this vow is based on the premise that usurped money legally remains the property of its owner. You must fulfill your vow if Allah returns this money to you, and you are not obliged to give an equivalent amount as charity. This money of yours is not unlawful, for Allah does not accept charity from unlawful money.