A lot of these companies set up tax efficient achemes (under the old rules) whereby the contractor was employed by an offshore company (usually in Jersey, but anywhere but UK would work).
They would get paid into offshore company, and only be taxed in Ireland on earnings actually brought into the country. This would only work if they did not need to remit all of their employment income to live on.
In the case of a UK individual, if, for example he was reniting out his UK house, that income would be taxable in Ireland anyway (whether brought in or not), so the UK people would remit their rental income to live off in Ireland, and could usually leave a big chunk of earnings outside the UK and not be taxable in Ireland as it was not remitted, and not taxable anywhere else as they were not resident there.
The changes in tax rules certainly put a stop to this type of tax planning!!
However, these companies are still in business because they now merely deal with the admin, accounting and tax for contractors - but I don't believe there are any great tax savings to be made that another accountan't couldn't deal with.
Let me know if you are offered any other "schemes" I would be interested to know what they are.