Ms Jones was leading a debate in Parliament on PIPs in Wales.
According to official Government documentation, the purpose of PIPs "is to help towards some of the extra costs arising from a health condition or disability.”
It is the replacement for Disability Living Allowance which has been put in place by the current Government and can be used to cover transport, care and all sorts of other costs that can be vital to those who are disabled or sick.
In her speech, the MP said: "We are talking about failure – paid for by the taxpaying public – being subsidised on a massive, multi million pound basis.
"Somehow, somewhere, someone has to carry the can for what has happened here as the result of a deal between a private company and the Government."
after the debate, Ms Jones said: "The current system is a mess and urgently needs to be sorted out.
"Ordinary people do not pay their taxes for this sort of incompetence."