If someone rents a ship he may commit himself to paying for the ship if it breaks besides paying rent as long as he doesn't have to pay if the ship goes down in value.
It is permitted to rent out a metal utensil even though the renter is paying the rent and he is also obligated to pay for any metal that is rubbed out as long as he doesn't have to pay for the depreciation of the metal that is not rubbed out. (1)
It is permitted to give money of orphans to a person to invest on condition that the investor will be responsible for any losses and the profit will be divided between them. (2)
R. Yosef says that the money of orphans shall not be invested by the Beis Din and instead the Beis Din shall give the orphans an allowance from the money.
Rabah says that the money of orphans shall be invested by the Beis Din with a rich person who owns chunks of gold on condition that the profit will be divided between them but any losses are the sole responsibility of the rich person. (3)
R. Ashi says that the money of orphans shall be invested with a person who owns property without any claims on it and he adheres to the Dinim of the Torah and is never excommunicated.
A person may accept sheep from a non-Jew to raise on condition that he is responsible for the animal if it dies or is lost and the profit will be divided between them, but it is forbidden to accept it from a Jewish person. (4)
It is permitted to borrow and lend money to a non-Jew or to a Ger Toshav (a non-Jew who keeps the seven Mitzvos Bnei Noach) with Ribis
Someone who accepts sheep from a non-Jew to raise even if the Jewish person is responsible for the animal if it dies or goes down in price the animals and the offspring are Patur from Bechorah. (5)
A person who borrows money with Ribis transgresses a Mitzvos Aseh and Mitzvas Lo Sa'aseh.
A person should only lend money with Ribis to a non-Jew if he needs the money for his essential necessities.
A BIT MORE
1. If the renter was also paying for the depreciation of the metal that is remaining it would be Ribis because since he is responsible for the depreciation it is tantamount to a loan and the money he pays for rent is Ribis.
2. This is only permitted for orphans but not for adults because it is Ribis d'Rabanan, however the Rabanan permit it for orphans so that their money will not run out
3. A person who owns chunks of gold is certainly rich because chunks of gold are not usually gives as a Pikadon and therefore there is little concern that he will default on the loan.
4. Since it is half loan and half Pikadon even if he wasn't totally responsible for the losses it would be Ribis because he is taking care of the half of the Pikadon in return for receiving the loan therefore certainly in this case that he is totally responsible for the losses it is forbidden.
5. Since if the Jewish person doesn't pay the money that he owes the non-Jew the non-Jew will take the animals and if he can't find the animals he will take the offspring and since the non-Jew has a hand in the animals it is Patur from Bechorah.