Now, the UK is still in the EU, so it works just as it has for the last 15 years or so, or at least it is supposed to.
To preserve the rights of EU citizens after the UK leaves the EU, they have devised the EU settlement scheme. This should take care of most of your concerns:
If you’re an EU, EEA or Swiss citizen, you and your family can apply to the EU Settlement Scheme to continue living in the UK after 30 June 2021. If your application is successful, you’ll get either settled or pre-settled status.
The EEA includes the EU countries and also Iceland, Liechtenstein and Norway.
You may be able to stay in the UK without applying - for example, if you’re an Irish citizen or have indefinite leave to remain.
As the last paragraph notes, Irish citizens are not required to sign up for the settlement scheme. They have a right to live and work in the UK that is independent from EU freedom of movement:
Who does not need to apply
You do not need to apply if you have:
- indefinite leave to enter the UK
- indefinite leave to remain in the UK
- British or Irish citizenship (including ‘dual citizenship’)
- What happens if Brexit happens between the present moment and the actual start date?
There will be a transition period, which is currently set to end at the end of next year:
If you’re an EU, EEA, or Swiss citizen, you can continue to use your passport or national identity card to prove you can work in the UK until 31 December 2020.
If your start date is after the end of the transition period, you will need explicit permission to work.
- What happens if Brexit happens sometime after the actual start date but before all the paperwork is in order?
In that case you should be fine. The deadline for applying for the settlement scheme is currently June 30, 2021, or, if there is no deal, December 31, 2020:
When you can apply
The EU Settlement Scheme is open. You can apply now if you meet the criteria.
The deadline for applying is 30 June 2021.
Which status you get may depend on when you apply.
If the UK leaves the EU without a deal
You will need to be living in the UK before it leaves the EU to apply. The deadline for applying will be 31 December 2020.
- Is it possible that the EU citizen will have to give up the job?
The risk is higher than it would be for a UK or Irish citizen, but it is very small.
What are the risks that one runs by signing up for a UK job now?
This is quite broad and speculative, but the risks are small. The most likely troubles are probably related to likely administrative confusion with respect to the new status and the qualifying criteria.