What should one do if they have lost money in a business venture and their partner is now demanding payment, which they are unable to provide, and they fear writing a promissory note (waṣl amānah) due to concerns about its misuse, despite their intention to repay when circumstances ease?

If the loss was due to negligence or dereliction of duty, you must pay the right to its owner. It is not permissible to refuse to write the document, because it is a means of proving the debt, and your fear of the document being used against you is unfounded. If you are well-off, you must pay the right immediately. If you are in straitened circumstances, he has no right to harass you, and the document proves the right against you, to be paid when you are able.