the legal way is, your child must keep own country citizenship all the way.
inform ica and mindef your kid is renouncing pr by 11. so immigration may switch to dependent pass, or deny living in sg. yes got ppl kid live in johor but everyday go sg study.
technically 13 is the cutoff age, but you must not collect any benefits (i.e. school/healthcare/etc subsidies) from 11.
renounce liao then go apply study pass or work permit when kid grow up and want to hang around sg.
the not-so-legal way is, keep pr all the way, but when kid kanna ns, make noise about immigrating and renouncing citizenship. not so good chance of getting released (though i saw a couple of cases ppl serve 2-3 months then immigrated out). not good chances getting any sg work visa in the future, but can return for holiday.
the illegal way, is keep pr all the way. send kid to overseas uni at 16. ns letter come act blur ignore. can also forget about coming back sg for anything, unless you're a pianist or something.
learn from expatforums one. they got all sort of story there.
wait... why are you getting pr in the 1st place if you don't want pr in the 1st place?