How to deduct monthly payments to pay off debt in closed foreign business?

tricky question.

the part of the payment that relates to the principle on the debt owed isn't directly deductible. what happens is that the capital gain or loss on the closing of the whole business goes to schedule D -- IF you were subject to US taxes at the time, and possibly IF a few other things. you'll need to verify that there is any deduction at all by reading the IRS' publications. [see irs.gov for all pubs and forms]. This had to be done in the year in which the loss was realized (YES -- way back then).

don't forget that any foreign tax benefits realized may have to be accounted for and reported as a negative item on Form 1116 -- credit for foreign taxes paid. [you can't get a deduction benefit in both countries for the same loss, only the larger of the two benefits split between the two countries.]

then, IF the capital loss does go onto your US taxes, the interest can be discussed.

Offhand, I'd say that it is similar to any other investment interest expense [like margin interest from the stock market], and thus deductible only when such investment interest is deductible. see Form 4952 and instructions plus publication 550

[the likely summary answer is mostly against other investment income and only then.]