i've had three vehicles that fit the category you describe. the first 2 were a 12 year old chrysler i picked up from a funeral home with only 40,000 miles on it. the second was a 9 year old plymouth sedan from elderly friends of an aunt with 45,000 miles on it. in both cases i presumed maintenance had been followed due to who the previous owners had been and in both cases i had lots of problems.
the third vehicle was a 20 year old pontiac sedan with 55,000 miles on it. with this one i knew the car had been stored for several years as part of an estate so i spent some time and money up front. i had the garage go thru it when they were safety checking it and change ALL the fluids, front to back, do a complete tuneup and check for any sign of leaks. they replaced the valve cover gaskets, hoses and since the rad didn't look healthy i stuck another one in. i drove the car 40,000 miles and the only unexpected problem i had was it blew a water pump. by the time i sold it it it puffed out a bit of smoke at start from worn valve seals( my guess) but still ran good.
if i was to look at another lo miler again, i think i'd spend the money up front and go over it bumper to bumper with the basics like last time. it'd be a worthwhile investment in the long run.