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When someone dies, any money owed to them is counted as part of their 'estate' (everything they own or are owed less anything they owe). It's the responsibility of the executor (if there is a will) or administrator (if there is no will) to collect debts owed to the deceased.
If the deceased was owed money (for example, for something they sold to someone) and there was an agreement in writing, this may be enforceable by the executor on behalf of the estate. If, however, the arrangement was on a casual basis this may be difficult to prove and it's unlikely that the debt will be recoverable.
If you're having difficulty recovering a personal debt owed to a deceased person you should seek independent legal advice (see where to get help and advice')
The legal situation regarding business debts owed to the deceased - including rental and hire purchase agreements - depends on whether the business is a sole proprietorship, a partnership or a company. Sorting out business debts can be complicated, so it's important to get legal advice (see 'where to get help and advice')
You can get free, independent advice on recovering debts from a number of organisations such as the Citizens Advice Bureau (CAB), Age Concern and Community Legal Advice.