It is widely held that attenuated live-virus vaccines are the best vaccines, at least for respiratory diseases, because they are able to induce an IgA response. Plus, nearly all viruses enter the host via mucosal surfaces (oral cavity, nose, gut, lungs), where the first line of defense includes IgA.
Poliovirus is the exception that proves the rule. Polio grows extensively in the intestine, hence its transmission by the fecal-oral route, resulting in a unique epidemiological role for swimming pools in advanced countries. However, polio doesn't seem to cause much pathology there. The major trouble occurs when it moves to the nervous system.
OPV (oral polio vaccine) induces IgA while IPV (inactivated polio vaccine) does not. This restriction is not a serious problem for the inactivated virus vaccine because it seems that IgG is sufficient to prevent polio's movement to the nervous system.
There is some prospect for development of adjuvants that would drive B-cells to switch to producing IgA. One of the best understood is cholera toxin, where binding to certain cells stimulates IgA-promoting cytokines (IL-1, IL-6, IL-10). However these are too toxic for use in humans. Perhaps someday we'll understand enough to be able get an IgA response with a killed virus, but that moment has not come yet. ref
Virus attenuation
We are left with the fact that historically, live virus vaccines have mainly been produced via attenuation. We can look at some modern approaches elsewhere, like smallpox or adenovirus or retroviruses that are already attenuated and can display viral antigens.
Yellow Fever (YFV) virus ("the black vomit") is now a disease of the tropics, but it was once common in the US. 10% of Philadelphia's population was lost in an epidemic in 1793, and even more in New Orleans some years later.
In the mid-1930s, Max Theiler found that YFV could grow in mouse embryos. So it was passaged from one mouse embryo to another, and then it was found that, somehow, the virus acquired the ability to grow in chicken embryos. So one general approach is to try to grow the virus in some kind of cells (anything): human, if necessary, or monkeys or mice and then adapt them to grow in chicken cells.
The chicken cells can either be in a whole embryonated hen's egg (i.e with a growing embryo), or cells growing in a culture dish. Here is a picture showing the different sites within the egg that are suited for different viruses (I believe these are mostly viruses that have been adapted to grow in eggs already).
I haven't read enough to know, but I would suspect that cultured cells for virus were usually CEF (chick embryo fibroblasts), which are easy to prepare. You mince the embryo, first removing the head, and put the pieces in culture. A few days later you harvest the growing cells by treatment with the enzyme, trypsin. A few cells are transferred to a new flask. Now, you have fibroblasts which will grow for a number of generations, and no more embryo. These are called primary cultures.
Today a number of cell lines have been derived from chicken that will divide forever. There is a famous cell line from humans called HeLa which you may have read about.
The measles virus (MV) was first grown in human kidneys in tissue culture, then in human placentas in tissue culture, and then in chicken eggs. Later, it was adapted to primary cultures of CEF. In rare cases cells derived from an aborted human embryo have been used.
Another approach is to adapt the virus to growth at lower temperatures. Due to paywall restrictions, I haven't been able to read much of the literature on this, but I believe it was done in CEF growing at 25°C. There is a well-known influenza live virus vaccine of this type.
So, a virus that normally infects humans and causes disease is adapted to grow in chicken cells, or adapted to grow at 25°C instead of 37°C, or both. Afterward, you may find that the procedure yields a virus that no longer grows very well and does not cause disease in humans.
This may be because a virus can specialize in one or the other but not both. Or it may be that during prolonged replication mutations accumulate that affect grow under the original condition, but these are not selected against as they would be in the original host or at the original temperature.
Molecular biology
Surprisingly little is known about the molecular basis of attenuation. Probably that's because such work requires a system for reverse genetics. That would be some DNA-based clone where the mutations to be tested could be introduced, followed by a method to produce the live (typically RNA) virus. I've written about a new system of this type for SARS-CoV-2 where the clones are maintained in yeast.
In addition, the gold-standard would be to test the virus in primates like monkeys. That's really expensive and would need to fully justified. Without a strong need to know, it might be hard to get approval for such a study today.
One case where new antigens are substituted into an attenuated virus is the live influenza vaccine.
Influenza is a segmented virus. If two different strains of influenza infect the same cell, you can get reassortment. Suppose we start with a known attenuated mutant (due to changes in PB1 and PB2), and coinfect with an influenza virus whose HA and NA we want in the new vaccine. Just take the progeny viruses, clone them (propagate descendants from isolated single viruses), and then choose the one with the right genes: PB1 and PB2 from virus 1, and HA and NA from virus 2.
In summary, attenuation has been widely used but is still more magic than science. The best thing would be if an attenuated vaccine for the original SARS had been developed. Then you could just substitute the new RBD (receptor binding domain) and try it out. Unfortunately, it doesn't seem that was ever accomplished.
