Do tension pulley's go bad

If we had the engine size that would help .. IF it has the V/6 engine - many times the novice DIYer will mistakenly assume the 'water pump' is the belt tensioner due to it's physical size and location on the engine .. IF you're seeing antifreeze leaking in that vicinity, it will cause engine overheating.. In any event - qualified personnel at local auto repair facility will need to evaluate this for you.