I asked this question over on the beginner bikers forum, but I'm not getting much action over there so I'll ask it here, too. I'm looking at a 2005 Yamaha Road Star with 40,000 miles on it. It has aftermarket exhaust pipes and the owner doesn't know if the carburetor has been rejetted. Is it likely to have some sort of engine damage if the carb has not been rejetted?
First off, if you are buying a motorcycle that has been modified always ask the original owner for the original parts. It's not just the best way to get a bike running like when it was new again, it also may become necessary if the motorcycle ever needs to pass emission standards testing or inspection. 2005 is a new enough model it actually comes under federal EPA vehicle laws that make it illegal to default pollution control devices on a motor vehicle intended for street use, the original exhaust may be considered part of that emission control equipment unless the aftermarket exhaust bears compliance markings.
The carburetor on that bike is a CV (constant vacuum) type carburetor which is the most complex form of carburetor ever devised, it contains as many as 5 fuel circuits including the mechanical fuel pump that is on there to stop it from back-firing on deceleration. CV carburetors found application on street motorcycles strictly for the purpose of meeting the emission requirements of the time, not because of performance or cost considerations. CV carburetors are also all but extinct on current motorcycles and that technology is being eclipsed by fuel injection, which better meets todays even higher pollution control requirements as well as performing much better, particularly if the motorcycle is used seasonally and stored for periods of time long enough to have old fuel evaporating inside the carburetor float bowl chambers, which fuel injection systems do not have.
The CV carburetor attempts to make the motor run as lean as possible in order to reduce fuel consumption and the additional resulting emissions associated with unburnt fuel. Putting a 'performance' or freer breathing exhaust on the motorcycle makes the already lean operating condition even more lean, so the bike probably will run poorly or not at all if the carburation was not altered at that same time as the exhaust. On a great many CV carburetors the low speed jet will be sealed to prevent adjusting which is considered tampering with the emission compliance. That seal is often removed on bikes that have been fitted with modified exhausts and that would be your first indication that the jetting has been altered.
To the question: "Is it likely to have some sort of engine damage if the carb has not been rejetted?" It is likely to run extremely lean or not at all if the carb was not adjusted to compensate for a change in the exhaust system. Extremely lean operating conditions will make an engine run very hot which can potentially be harmful to the exhaust valves, piston and spark plug, which is why previous posters suggested you should read the plugs. That is a good place to start and a compression test will tell you even more.
Good luck with your motorcycle
and make sure your next motorcycle purchase comes equipped with a computer controlled fuel injection system.