Is it permissible for me to perform the Hajj pilgrimage while I owe a debt to a deceased person?

If the debt's term has expired, then it is obligatory to repay it. If there remains enough money for Hajj, then you perform Hajj; otherwise, it is not obligatory upon you, because Hajj is only obligatory upon the one who is able.

If the debt is deferred, the majority of jurists hold that the death of the creditor does not make the debt immediately due; rather, the term transfers to the heirs.

If you hope for the debt to be repaid at its due date, then you may perform Hajj and postpone the debt repayment. Otherwise, prioritize repaying the debt over Hajj.