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Should I sell my home in negative equity or rent it out?
In summary, you are getting €12,000 in rent.
You are paying interest of €3,000
So you are making a profit of €9,000 a year before other costs.
If property prices don't change, you will have paid off your negative equity in around 10 years and you will then have a very profitable investment and an asset. If prices rise, you will reach this situation earlier.
If you are going bankrupt for other reasons, i.e. other debts, then fair enough. But you should not be going bankrupt over this profitable investment.
Have been given free money from family till now, but would like to stop that if I can.
Within a decade, you will have a profitable investment and an asset and may be in a position to repay this money.
What chances do I have to get a deal (aka debt write off) from the bank?
Very little indeed. As you are based in the UK, ptsb should be happy enough to allow you to sell this and should write off the shortfall given the real threat of UK bankruptcy. But the attitude of the banks when threatened with bankruptcy is: OK, fire ahead.
So ask them, but expect to be refused.
Then ask them if you can sell the property. The bankruptcy will be much more straightforward if the Official Receiver has to deal only with unsecured debts which is what the mortgage shortfall would become.