Earlier quoted context omitted.
They will make concessions. I'll put money on it. The UK leaving with no deal would be the beginning of the end of the EU. There is already growing anti-EU sentiment in Italy (4th largest economy in the block), Hungary, Austria, Poland. The UK leaving could set off a chain reaction which would either end the EU project or drastically reduce its size. The EU simply can't afford to have the UK leave completely, because…
That sort of assumes that the UK is all hunky dory after it leaves. If it gets slammed with an immediate recession/raising unemployment/etc... then that's leverage the EU has to convince other members to stay.
The UK has a lot going for it. It might not be hunky-dory immediately after leaving, but there's plenty to suggest that the UK will do just fine in the medium to long term.