Is there sin incurred by not paying a sum of one hundred dinars resulting from a sponsorship of an orphan that could not be completed?

If the committee allocates the shares of each donor to a specific orphan and does not disburse to him except upon receiving the amount from the donor, then there is no sin upon you for not paying the remaining amount, unless the sponsorship was a vow, in which case it becomes obligatory due to your statement. If you are unable to fulfill it, then an expiation for a broken oath (kaffarat yamin) is required from you. It is better to pay the amount if possible, even in installments.

However, if the committee pays the orphan from its own funds and has already paid your orphan with your permission, then this amount is considered a debt from you to the committee, and it is obligatory to settle it by payment or by seeking their release from the debt. Therefore, you should communicate with the committee to be absolved of the debt, or to pay the amount in installments, or to be absolved of a part and pay the rest.