Hi Planningnow and welcome to the forum
Assuming that the legal documentation regarding your parents security was properly drawn up, and registered at H M Land Registry, then their interest in your property is valid and they would be paid in priority to the unsecured creditors.
If you choose bankruptcy as an option, and there is no equity, then it is unlikely that there would need to be a sale of the property - and you could get your parents to acquire your beneficial interest for a nominal sum - usually £1 plus the legal costs of transfer.
If you are going to rent the property out - make sure that the rental you will receive will at least cover the mortgage, buildings insurance and maintenance costs. And bear in mind that if you lose your tenant you will still have to pay the mortgage.
Regards, Melanie Giles, Insolvency Practitioner for over 20 years.
For further details contact me at
http://www.melaniegiles.com and view my IVA blog at:
http://melaniegiles.blogs.iva.co.uk