He put the funds of the charity into a mudaarabah scheme and lost the money

Firstly: 

If a person invests the wealth of another in a mudaarabah partnership, then the profit is to be shared between them according to whatever they agreed upon, and loss is to be borne by the owner of the money; all that the worker loses is his work and his effort. It is not permissible to stipulate that he should bear any of the loss so long as he has not been negligent. If he is negligent or he goes against what is stipulated and that leads to loss, then he is liable. 

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (5/22): Loss in the case of mudaarabah is borne by the owner of the money only, and the worker does not have to pay any of it, because the loss is a decrease in the capital, which belongs only to the owner, and the worker has nothing to do with it. So the loss is taken from his (the owner’s) money and no one else’s. They only share whatever profits are earned. End quote. 

He also said: If it is stipulated that the mudaarib (the worker) is liable for the money or a share of the loss, then this condition is invalid, and we do not know of any difference of opinion concerning that, although the contract is valid. This was stated by Ahmad. It is also the view of Abu Haneefah and Maalik. And it was narrated from Ahmad that the contract is rendered invalid by that; he narrated that from al-Shaafa‘i. That is because it is an invalid condition, so it renders the mudaarabah invalid, which is similar to the case if there is the condition that the profit will be for one of them only. End quote from al-Mughni, 5/40. 

Secondly: 

If the director of the institute thought on the basis of his own opinion that some interest was to be served by investing some of the institute’s money – other than zakaah funds – and the market was stable such that there was no risk involved, then there is no blame on him in the event of loss, because he was only seeking to serve a general interest and did not do anything that is regarded as negligence with regard to what was entrusted to him. 

But if he acted hastily or negligently, or he was not allowed to invest the money, then he is liable. 

The scholars of the Standing Committee for Issuing Fatwas were asked: 

This cooperative has some money that is frozen in the bank and it is not being used in any beneficial way; this is after completing some services that the group was required to provide whilst keeping this money aside for emergencies. As we want to get some halaal returns, we thought of delegating one of the financial or commercial companies to use this money in the kind of business that it does, such as buying and selling building materials such as iron and cement, and giving us the unspecified profit, whilst stipulating that the materials that are bought and sold during a specific period should be declared and the agent will take some wages for doing the buying and selling. We hope that you can advise us whether this action, which is aimed at making use of the money regarded as a trust borne by us to serve the interests of the Muslims, is permissible. May Allah reward you with good. 

They replied: 

If the money mentioned in then question is zakaah funds, then it must be given to those who are entitled to it according to sharee‘ah once it reaches the cooperative. But if it is not zakaah, there is nothing to prevent using it for trade in the interests of the charity, because that brings more benefit for the cooperative and those who are supporting it. End quote. 

Fataawa al-Lajnah al-Daa’imah, 9/403 

And Allah knows best.