My pension is not frozen.
I don't think they will be able to obtain a Resident's Permit straight away. The first step is to apply for a Visitor's Permit which, for EU citizens, will normally be for 4 or 5 years. This is quite a bureaucratic process. The applicants must take with them originals for each person and a photocopy of each: passports, 2 passport photos, details of all visits to Cyprus for last 5 years, all up-to-date bank statements and investment details (e.g., share certificates), statement of all income (royalties, annuities etc.), deeds or contract of purchase of any property in Cyprus or contract of house rent, certificate of medical insurance and anything else that demonstrates that you are solvent and not likely to become a burden to the Cypriot State. After a few months, you will receive the famous "pink slip" to attach to the Alien's Visitor Permit.
They can apply for Resident's Permits after about three years with pretty much the same documentation. I recommend they do this at least 18 months before the pink slip expires, otherwise they may have to renew the latter before the new Permit is issued. This procedure is fairly similar, except that you will also be invited to attend an interview at the District Office by the person responsible for the municipality where you reside.
There is a saying that the Brits invented bureaucracy, the Colonials improved on it but the ex-Colonies perfected it