Say that an American gets imprisoned in a foreign country. The American government presses the foreign country's government to release them and comes to an agreement under which the latter will release the imprisoned American in exchange for the former releasing a prisoner of the foreign country.
However, the imprisoned American comes to know about those terms and strongly objects to them for some reason. Perhaps they had previously heard of the other foreign prisoner's case, perhaps they or someone they know have been personally affected by the foreign prisoner's actions, or perhaps they may be morally opposed to the idea of the U.S. releasing someone in exchange for their own release. In either case, the American prisoner would prefer they stay behind bars in the foreign country if releasing them would mean the release of the foreign prisoner and they prefer the other prisoner remain behind bars as well.
Can the American prisoner insist that the other prisoner not be released and that they're OK with staying imprisoned themselves? Will the American government honor the request and decline to release the foreign prisoner since the American prisoner objected to it?
As an example, say that in Brittney Griner's case, she had been closely following the news when Viktor Bout got convicted and jailed and strongly agreed with his prison sentence, or someone who purchased weapons from Bout went on to murder or injure someone close to her and so she's biased toward him remaining in prison. If she's OK with herself staying in the Russian penal colony if it means Bout will remain imprisoned, can she voice her objection, and will the American and Russian governments respect it?