Is the wife's sister entitled to claim a refund of the amount she paid for the project, given that she was the first to withdraw from it, and the other partner incurred significant financial losses that led to the project's closure?

Losses in a company are borne by both parties according to each one's share in the company's capital. It is not permissible for one party to make the other bear the loss or part of it, unless one of the partners transgresses or is negligent with the company's assets, in which case they are then liable for the loss.