The Iron Bank of Braavos and Dragonstone!
I know that, in Game of Thrones, Stannis Baratheon was the lord of Dragonstone for a long period of time. When he failed to conquer King's Landing the first time, in "Blackwater" (Game of Thrones, S02E09), he chose to go to North as guided by Melisandre (aka the red woman) and Ser Davos.
Ser Davos tells him that they can go to the Iron Bank of Braavos and get some funding to hire sellswords. At the time of discussion with the Iron Bank, they ask Stannis that how would he pay back his debt.
Afterwards, Stannis lost against the Boltons and was killed by Brienne of Tarth. Who is going to pay the Iron Bank now? The Iron Bank has the right to claim Dragonstone.
Short answer is no one is going to pay debt of Stannis.
Stannis and Davos convinced Ironbank based on their claim to throne and by telling them Stannis is the only hope to get their money back form Iron throne as well. Here is the conversation between davos and Tycho Nestoris at Iron Bank:
Davos: He's an honest man and he's your best chance to get back the money you've sunk into Westeros. Which is a lot, I imagine. Wars are expensive. Who's the real power in King's Landing?
Tycho: Humor me.
Davos: Tywin Lannister. How old is Tywin Lannister? 67. 67. And when he dies, who's in command? A half-grown boy, the product of incest? Cersei Lannister, a queen whose people despise her? Jaime Lannister, a man best known for killing the king he was sworn to protect? When Tywin's gone, who do you back?
Tycho: That is a problem for another time.
Davos: Begging your pardon, I think it's a problem for now. There's only one reliable leader left in Westeros. Stannis. He's got the birthright. He's in his prime. He's a tried and tested battle commander. And he doesn't just talk about paying people back, he does it.
They never kept Dragonstone as security so there is no question of Ironbank claiming it.
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What was the Iron Bank?The Iron Bank of Braavos (located on the fictional continent of Essos) is an incredibly powerful and wealthy institution, lending money to governments and military commanders.
What happened to the Iron Bank of Braavos?After the Sack of Highgarden, the gold needed to pay back the Iron Bank is sent by Jaime from Highgarden to King's Landing. Pleased with Cersei's progress, Tycho promises that Cersei may take out a new loan when the previous one has been paid with the Tyrell gold.
Who created the Iron Bank?According to Matthar, the Iron Bank was founded by sixteen men and seven women who hid valuables in an abandoned iron mine shortly after the foundation of Braavos.
How does the Iron Bank of Braavos work?Business model: The Iron Bank is a lending powerhouse, often funding both the Iron Throne and rival throne seekers. Even other banks borrow from it. The Iron Bank is known for funding the enemies of rulers who don't pay their debts.
The Iron Bank - Game of Thrones Season 4 Histories and Lore
More answers regarding the Iron Bank of Braavos and Dragonstone!
The Iron Bank has the right to claim Dragonstone.
Mortgages do not exist for the Iron Bank (not in this sense, at least).
In real life, mortgages are a way to settle a debt that the debtor is refusing to pay, without having to resort to violence. In essence, you sign a contract promising to give away your property should you fail to pay the debt.
However, the Iron Bank can (and will) use violence. Violence is not only still actively used, but it is also accepted more (e.g. flogging, torture, armed combat), it still exists even in legislature (trial by combat).
Tommen tries to remove the legal option of trial by combat, and while Tommen honestly believed that it was done because it's needlessly barbaric, in reality it was a ploy by the High Sparrow to prevent Cersei from escaping justice by using the Mountain to fight for her and basically acquit her from her crimes.
Mortgages are not needed if you're allowe to use violence against debtors who refuse to pay you back. So let's discuss the Iron Bank's strategy to ensure that debtors will pay back their debt.
1. Are you likely to be able to pay back your debt?
Are you asking for a loan that you will never be able to pay back? Are you considered capable enough to actually achieve what you want and be able to pay the Iron Bank (including interest)?
If not, you won't even get the loan to start with. But let's assume that the Iron Bank gives you the loan because you are a wise investment.
2. You stop paying your debt.
If this is a temporary issue, and you will soon be able to resume the payments, the Iron Bank may grant you an extension (more interest for them to collect).
If this seems to be a permanent issue, then the Iron Bank takes action. Their favorite way of doing so, especially for loans extending to (would-be) kings, is to start financially supporting your opponent.
The main goal of the Iron Bank here is not to collect your outstanding debt. But rather, the Iron Bank uses revenge, thus ensuring your quick demise.
They do manage to recover some money, from the interest that the opponent pays them.
This approach is intended to breed fear into the next people who ask the Iron Bank for a loan, who will be less likely to enter into a loan agreement if they might not be able to pay you back.
This is corporal punishment. Teachers and parents use violence against you when you misbehaved, so that you wouldn't want to misbehave again (fearing the pain). This would also work by proxy. If your sibling gets a beating, then you will be afraid too. And that's what the Iron Bank does. It punishes one, so that the others are now afraid and more likely to fall in line.
It's not impossible for the Iron Bank to lose money in the short term. This was the case for Stannis. However, you should consider the Iron Bank as "playing the stock market", backing claimants to the throne (as opposed to companies).
While the Iron Bank can potentially lose money on a debtor here and there (Stannis), they will always come out ahead in the bigger picture.
Tycho Nestoris often speaks of "wise investments", and he means "giving money to people who are likely to pay it back with interest". There's no guarantee, but they back the right people more often than not, enough that they actually make a profit.
There is nothing to be paid. Stannis has no debt, no loan from the Iron Bank.
In season 4 episode 6, Stannis and ser Davos visit Iron Bank. Their request for loan is declined by the Iron Bank:
You can see why these numbers seem unlikely to add up to a happy ending from our perspective. I'm afraid we must respectfully decline your request.