He's an 'eligible bachelor'. [=an unmarried man who would make a good husband]
He's 'eligible for' health insurance through his employer.
He won't be 'eligible to retire' until next year.
(..) - Go on. - So, just sit back and relax, my lord, because it's time foryou to meet today's eligible bachelorettes. And here they are! - . . . (..)2001 Shrek