Hi Peony
Your understanding of arrears is correct.
If your mortgage balance was €200k and the interest rate was 5% and you paid nothing for 10 years, then you owe €325k today.
If they tell you that your arrears are €150k, this is simply a memorandum figure. If you pay them €150k, you will reduce the balance to €175k , which is the balance it would have been had you made all your payments on time.
If you clear your arrears and the property is in positive equity, you are free to do what you want with the property. Keep it or sell it.
Brendan