Yes, he can, depending on the country, and without investing in a business or property. Retirees have a certain advantage, as they're not going to work (or allowed to) and their income will support the local economy. Spain, for example, has a retirement visa scheme. For France, you have to apply for the carte de sejour from your home country before relocating. Italy has an elective residency visa for foreign retirees. Generally, you have to prove financial means (significant is an advantage) and medical insurance coverage and, in some cases, a rental agreement. There may have additional requirements, such as a health exam or criminal background check. Once established as a resident, the expat retiree may become eligible to access the country's national health plan, such as in France and Italy.
And a suggestion, have your relative outline his requirements, such as cost of living (including cost and availability of rentals), ease of access (major airports, need for a car, ground transportation), local expat community, healthcare facilities, climate, language. In my own planning, I found it easiest to search 'country' and 'retiree visa.'