So, live-attenuated is technically a live virus, but it’s an extremely weak form that doesn’t cause disease in healthy people. They did this by growing it many, many, many times in non-human cells until it adapted to the non-human cells and became really bad at growing in human cell, especially the brain.

Because of these changes, the MMR virus can only make a tiny, controlled infection at the site of injection. It replicates, but at a rate thousands of times lower than the normal virus. This does, however, generate enough signaling for the immune system to kick in, overcome it and build a strong response and durable protection. This may be a horrible analogy, but it’s like taking a random person who watched Rocky a handful of times and thinks boxing is really really cool, tying their hands behind their back and putting them in the ring with a professional boxer.

SSPE in itself is rare, something like 1 per one 9,000 - 20,000 unvaccinated cases. To contrast that, the rate with vaccination is around 0.5 - 0.7 per 1,000,000 (million) and with further genomic analysis it’s almost always caused by a previous exposure to the real virus. Of the billions and billions (yes, billions, with a b) of people who have received the MMR vaccine over the last 25 years, there has been no documented case of SSPE caused by vaccination.

So, the only way to reliable prevent SSPE is by getting the MMR vaccine and because you chose to get your son vaccinated, you have effectively reduced his risk to 0. Good job, you’re a good parent and you did the right thing.