Barbara and Colin Sellins, from Southborough in Kent, do not have any immediate family and wanted to make sure their funerals were paid for.
They have been told it is unlikely they will get back the Â£4,000 they spent.
A Kent Police spokeswoman said they were reviewing the Sellins' case and enquiries were ongoing.
"We are also in contact with both the liquidators and official receivers who are also investigating this company," added the spokeswoman.
Mrs Sellins said she found out Banham Funeral Services had gone out of business when she attempted to make contact to change a detail about her ceremony.
"We have worked hard all our lives. We don't owe anybody anything. We don't even have credit cards," she said.
"We have been left completely penniless. Who is going to bury us?"
The former management of Banham Funeral Services were contacted by the BBC but declined to comment. According to Companies House, the business was liquidated in May 2014.
Insolvency firm MHA MacIntyre Hudson, which was appointed to wind up the company's affairs, said "to date there have not been any assets realised and therefore no distribution to creditors".
Graeme McAusland, from the Funeral Planning Authority, said: "What should happen in a proper arrangement is, if a customer pays money over, that money is put aside in a trust or an insurance policy that is separate from the company that is selling the plan.
"That means it is ring fenced so if the company gets into trouble or goes out of business those assets are still there and therefore the funeral can still happen."
A couple who paid for their funerals in advance claim to have lost their life savings after their funeral director went out of business.