Is it permissible to give a portion of zakat to indebted friends who are unable to repay their debts, and is the zakat considered valid if one of them uses the money for purposes other than repaying the debt?

It is permissible to give Zakat al-Mal (charity on wealth) to indebted friends because they are among the categories eligible for Zakat, even if the Zakat does not cover all their debts.

If Zakat is given solely to an indebted person and not also to a poor person, and it is spent on something other than settling the debt, it is most likely not sufficient, because the indebted person does not possess the Zakat in full ownership. Rather, they spend it on the purpose for which they became entitled to it. If they spend it on something other than settling the debt, it should be reclaimed from them.

The recipients of Zakat are of two types: one type receives it for a reason that establishes permanent ownership (like the poor and the needy), and they may spend it as they wish. The second type receives it for a reason that does not establish permanent ownership (like the indebted and the mukatab - a slave who has a contract of manumission upon payment of a sum), and they may spend it only on the purpose for which it was given. If they spend it on anything else, it should be reclaimed from them.