] In 1813 Henry was made Receiver General for Taxes for Oxfordshire.

He was the public official to whom taxes are paid, and who in turn remits them to the Treasury. (I gather from various web references that Canadians still pay their income tax to the Receiver General.) Because he would have balances of public money in his possession, he would have to post a bond to account for and remit all that was due. I don't know whether, at this period, an RG was allowed to keep interest earned on the funds between the time collected and the time remitted. That had been the 18th century practice for government officers who held public funds, and it was a major perquisite of office. (Being Paymaster General of the Forces, for example, allowed the holder to draw interest on the Army and Navy payroll.)

] The inflationary war economy made things prosper. However, Waterloo brought deflation. The failure of the Alton bank of which Henry was a partner brought down the London bank of Austen, Maunde and Tilson in March 1816. No personal extravagance was attibuted to Henry . . .

That's typical. Prices usually fall at the end of a prolonged war, when government demand ceases to prime the economy. Debtors who have borrowed on the basis of wartime values can't pay, and if enough of them default, there is a banking crisis.

In JA's time there were no corporate banks except for the Bank of England. A banker put all his personal wealth on the line. He had unlimited personal liability to the depositors, and if the bank was short of cash because borrowers weren't repaying their loans, the banker had to make good its liabilities himself as far as he could. When the owners' capital is exhausted, the depositors lose their balances That's what happened to Henry, and since his sister had her royalties on deposit in his bank, that's what happened to her £13.