Bank chasing for outstanding balance

Yes, now, but I'm not sure when the law changed.

Historically, you could buy a house of €500k with a €400k mortgage, then if the housing market crashed and the house is only worth €250k, then you could hand the keys back to the bank and they couldn't pursue you for the additional €150k. However, that changed fairly recently (I don't recall when) and the banks can now pursue the vendor for the difference. I don't know if the law change applies retrospectively.

It's not a new law. Spanish banks have been able to pursue debts from British and citizens from other countries for many years, using international debt agencies. I can remember cases back as far as 2014 where people who just returned the keys to properties that they had a bank mortgage on, which was never cancelled or paid off, were receiving calls from international debt collecting companies. It works both ways too. A person with whom I worked, had his Spanish bank embargoed due to outstanding debts in the UK. They took a certain amount each month until the debt was cleared - and that was way back in 1998!

This has been legal for many years. In the early 2000s banks went after people for sure existing debt. People walked away from their property leaving the kets in the door and an outstanding mortgage. For example: mortgage owed 50,000 euros, bank sells property for 40,000 euros then chases original owner for 10,000 euros. 

Yes, that has been quite common here in .Spain and many other countrues, including Britain. The outstanding mortgage is 50,000, the bank sells for 40,000, outstanding balance is10,000, the bank then chases original mortgagee for 10,000