Just because you’ve had the chickenpox once doesn’t mean you can’t get it again. About 10% of the population can get it again. I’ve had it 4 times. Each time it was less severe.
There's no perfect protection. But what there is, is pretty good.
Having to deal with a son who was at risk of serious consequences from diseases other people regarded as minor has made me very aware of these things. He's now a healthy young adult - and is fully vaccinated, as it finally became an option once he was in his twenties (or at least, by then, he was strong enough to make the risk worthwhile if things went wrong), but we almost lost him three times in his teens - and if everybody around him had been immunised, two of those occasions would almost certainly not have happened. Other peoples decisions not to immunise their children put my son's life at risk. Despite that, I support their right to make that decision - but I also think it's reasonable for them to accept the consequences of that decision if it means their child might have to miss school increases the chance they will infect other people's children.
Chicken pox is actually in the same family as the herpes virus , and like herpes, the virus never completely leaves the body. The antibodies help deter further outbreaks, but in adulthood the virus often reappears in the form of shingles. If you have had chicken pox as a child, you have a much higher chance of getting shingles as you get older.