Enforcement proceedings are governed by the law of the State in which the EOP is to be enforced. The Applicant simply has to provide the designated enforcement authority in that State with a copy of the EOP, as declared enforceable, and with a certified translation where necessary.
If they travel anywhere in the EU the enforcement is governed by the law of the state in which the EOP is to be enforced. SO if an English couple are found to owe money in a UK court and a statutory claim is made against them in the UK and they refuse to pay then they can be declared bankrupt and an EOP is issued against them.
This makes their assets ANYWHERE in the world subject to the Official receivers demands.