They don’t just use dead or weakened viruses as their sole method.  There are three manufacturing techniques now – traditional egg grown virus, (mammalian) cell based incubation, and a recombinant process.  I am not very bright when it comes to this last process, so someone more knowledgeable than me will have to explain it, but it looks like they are using the DNA from the flu virus and combining it with another virus (baculovirus) to transport the DNA instructions to our cells that produce the antibodies.

Don’t you just love progress?

https://www.cdc.gov/flu/prevent/how-fluvaccine-made.htm