The carburetor on the typical two stroke motorcycle engine is extremely unlikely to fail, because it does it's complex job with very few moving parts, no stupid fuel pump, and with the fuel and the air both at atmospheric pressure.
Apart from the fuel and air, notable moving parts are the float assembly and valve, the slide with it's attached needle, and the spring between the top of the slide and the cap which returns the slide and needle to the closed position along with, or in the absence of gravity, when the throttle is closed. Those are the full time workers, the choke slide is a part timer who hardly has to do anything.
Because of that robust simplicity, carburetor failures are so unlikely that it's almost like worrying that you won't get to go riding because of a catastrophic number plate failure... In all the time I've had bikes and hung with groups of people who rode, I have never known "Carburetor failure" to stop a ride from taking place or end one suddenly with no way home. Both of those scenarios seem pretty remote, judging from my own experience and that of everyone I know.
But don't take my word for it, do a fun study of your own! - Go to "The Motocross Vault" on YouTube and dig up ALL of the great 2 Stroke motocross and supercross races you can find and watch them all. - You'll be waiting a REALLY long time (Forever) before you're watching a race and you see someone grind to a halt due to "Carburetor Failure". You'll probably be waiting even longer than that before you're watching a 2 Stroke race at the drop of the gate, and one guy's bike just sits there, engine suddenly dead due to "Carburetor Failure", while he kicks and kicks.
To see those kind of funny failures happen with some regularity, you have to fast forward to more recent Foopercross and Mowercross, and the handicapped, crutch bristling barges of today's weak scene. The complicated, stupid fuel injection systems that were supposed to be a bandaid and a shot of caffeine for the lumpy and flawed induction and power curve of the Fooper, fail like balloons in a preschool. I don't even watch modern pro MX and SX that much because of how boring it is, but I've seen Justin Barcia, Ryan Dungey, John Dowd and Vince Friese and many more pro riders each end up stranded on the starting line (Barcia more than once!) because their ultra-dependable Rube Goldberg fuel system crapped out suddenly..... And that was after a whole squad of professional wrenches had hunched over the junk for hours and days preparing! Where would that leave someone who doesn't have a squad of professional wrenches?
Oh... I can't WAIT for that trouble-free fuel injection!
His bike wasn't going anywhere.... And speaking of bikes that don't seem to be going anywhere...
I'm not trying to muckrake, but there's a lot of BS that people spew about all the problems "You're going to have", with a carbureted bike and they are almost always fairytales or miss labeled, unrelated problems. Then you get the same people singing hymns about fuel injection and making false comparisons that use Foopers or some "SS A.A.R.P." center console fishing boat engine as examples.
When Foopers with fuel injection were first introduced, the hype was "You'll never have to worry about anything fuel mixture related ever again, because the system with adjust to anything"
BUT, then that turned out not to be true, because the bikes needed to be adjusted to deal with heavy load conditions like deep sand and some other things like that, usually to richen the mixture and keep the operating temps from spiking so high that the pieces of crap would eat themselves alive .... SO they started including alternate couplers and other poo, so that those Fuel Injected Foopertroopers could "Re Jet" their bikes for those special conditions. ...So as it turned out, they still have to tune and "Jet" their Foopers occasionally, and they get a reduction in reliability and serviceability, an increase in weight, and an increase in cost in the not-a-bargain to go along with it.
And the hype that 4 stroke trolls like to harp on about how you CONSTANTLY have to keep trying to jet your 2 stroke.... Well, that's a load a manure too.
On a 2 stroke streetbike, do you really think you'd have to start by jetting your bike in Seaside Heights, then stop in Easton, PA and re jet because you gained some elevation, then stop again in Hazleton, PA to re-jet again??? No, you wouldn't... You'd be too busy just riding along and enjoying yourself.