You shouldn't need to appoint a trustee in bankruptcy, and that won't help if you do actually have a personal liability, which you may not in any event. Children are not generally liable for the debts of their parents, so unless you actually personally contracted for the funeral services, you are not liable for the debts. The estate of your father is liable for the debts before any distribution to beneficiaries, so this means you should apply whatever assets of the deceased there are to pay for funeral expenses and if these are insufficient, you would only be liable to pay the difference if you personally contracted for the funeral services.
Any other creditors should simply be told that the estate is insolvent, and if there is any money left over after funeral expenses are paid, it should be distributed to the creditors. Only if all debts and expenses are paid would there actually be a distribution of the estate.
Note, funeral expenses and similar are given priority over other debts under the Succession Act:
Finally, before simply accepting that the estate has no assets, you should make a determined effort to locate his superannuation, including any lost superannuation, as such funds can potentially be used to pay debts, and can be surprisingly substantial in some cases. It is also possible that such funds may include a life policy resulting in a substantial payout upon the member's death. I have personally dealt with a case where the daughter of a homeless man recovered a $50,000 death benefit arising from a life policy on her deceased father' forgotten superannuation, so it is worth investigating such matters thoroughly.
I trust the above assists.
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