If you are earning at least €31.000 Euros on an annual basis (whether based on a pension or any other kind of regular income) you can also apply for residency in Italy – though for non-working purposes only.
If more than one person is applying (for instance you intend to come with your spouse/partner and children) the income required will increase approximately by €7000 per year for each additional member.
Known as the 'Elective Residency' option for those seeking to relocate and become resident in Italy, you can also apply even if you do not have regular income, but simply deposit the same amount in a bank account during the time of residency, so over 31.000 Euros for 1 member and an additional €7000 (approx.) for each additional member.
Technically, the Italian government may check that the appropriate minimum amount is maintained in the account for the duration of the residency.
In order to apply for a residence permit for elective residency you must also have available an address in Italy as your residence here as well as Health Insurance: the Italian government provides a universal healthcare system that covers Italian residents, regardless of nationality.
However, Italian Elective Resident Visa applicants must show proof that they have their own qualifying health insurance. You should make sure that the health insurance plan can cover medical expenses (e.g., prescriptions, doctor visits, hospitalization and ambulance transportation) for at least 30.000 Euros per person per year and a minimum duration of 1 year.
After five years of regular residence, as well as compliance with the necessary minimum requirements, the holder of a residence permit for elective residence can apply for a long-term EU residence permit.
Even not being allowed to work in Italy that does not mean you will not be allowed to work in any other country provided you do not lose Italian residency by staying abroad working for longer periods of time than you spend in Italy.