Halacha forbids conducting business affairs, such as buying and selling, and making any sort of transactions, on Shabbat. The question arises as to whether this also applies to waiving a debt. As Hacham Ovadia Yosef discusses, there are two ways we can view the legal act of waiving a debt. One could view it as simply withdrawing oneself from the money, announcing that he no longer is interested in the money owed to him. From this perspective, waiving a debt is not a transaction at all; the creditor simply takes himself out of the picture, and the debtor can then keep the money. Alternatively, however, can view the creditor as granting the debtor rights to the money in question. And if we view it from this perspective, then this is, in fact, a transfer of property from one person to another, which is forbidden on Shabbat.
Hacham Ovadia rules stringently on this issue, noting that besides the possibility that waiving a debt constitutes a transaction, it also falls under the category of forbidden speech, as one may not speak about financial matters on Shabbat. The Hacham does, however, make an exception in the case of a poor person. If one waives a loan owed by somebody who is poor, this is considered Sedaka which is allowed on Shabbat. Otherwise, however, one should not waive a loan on Shabbat.
Summary: One should not waive a debt on Shabbat, unless the debtor is a person in need, such that it would be a charitable act.
