Is the income lawful or unlawful in a partnership where the machine broke down, and one partner refused to bear responsibility, whereupon the other partner continued working alone for years, then offered to return the capital and profits, but the other partner refused and forgave?

A worker in a job like yours is considered trustworthy (ameen). Therefore, you are not liable for the machine if it breaks down, unless it was due to your transgression (ta'addi) or negligence (tafreett). If it broke down without any negligence or transgression on your part, its owner is not entitled to anything from you. If he forgives you and waives his right, then you are absolved, and the money is permissible for you.