How is a partnership dissolved in the event of the financier's death six months after the agreement to finance livestock was contracted, and what are the implications of that for both the financier and the owner of the capital?

The mentioned transaction is a voidable ijarah (leasing/hiring contract) because the wage therein is unknown, and this is the most preponderant opinion. A voidable ijarah is rescinded, and in it, the employee is entitled to ajrat al-mithl (the equivalent wage), meaning what his counterpart would receive for similar work for a period of six months. This is to be paid to him if he is alive, or to his heirs if he has passed away.