It depends on the remaining LTV & whether the new bank want you!
Banks don't take it personally that you leave them, although they won't guarantee you the same rate you were on if you come back to them.
If you're in full-time employment, your outstanding mortgage is €50,000 and your house is worth €150,000 I doubt you'd have a problem switching.
If you just lost your job and are €50,000 in negative equity you haven't a hope in hell of changing your mortgage provider.