In a few years of tubeless ive only had one incident where the tubeless set up failed to work and that was when a spike punctured the tyre twice. One of the holes was right on the rim / bead which can be hard to get sealant to (especially when air is pissing out of another hole which im simultaneously trying to seal). Some punctures are harder than others to seal depending on type of puncture (thorn, tear, pinchflat) and location of puncture.
If your back home now and wondering how to fix your tyre if the sealant doesn’t work on its own you can use a bit of super glue, glue a patch on the inside, or use a tubeless repair kit eg sticky worms