A 10 yr old car with only 35k miles would have traveled only ~3,500 miles per yr, on average.
Cars which are used like that are almost always used for a lot of short-trip, local driving, and that tends to increase the probability of a build-up of sludge in the engine, as well as reducing the life of the exhaust system and the battery.
Then, to compound matters, many folks who drive very little–like that 3,500 mile per year driver–fail to recognize that maintenance should done on the basis of elapsed time, in addition to odometer mileage. They seem to not notice that…for instance…oil changes are supposed to be done every 6,000 miles or 6 months, whichever comes first, and wind up changing the oil every 6k miles–which is far too long for that type of engine abuse.
So…IF you can find one of those 3,500 mile per year cars that comes with maintenance records proving that maintenance was done at least every 6 months, then you might want to buy a car like that. Lacking records, I would avoid a car like that at all costs, due to the likelihood that the engine is filled with sludge and that other vital maintenance was skipped because of the low odometer mileage.
In addition to making sure that things like oil changes and trans fluid changes were done on the basis of elapsed time, make sure that any timing belt-equipped car that you buy had its timing belt replaced on the basis of elapsed time also. In most cases, this means replacement at least every 8 years.
Do NOT take anyone’s word that a car “has been well-maintained”.
Only trust hard copies of maintenance receipts.