When preserving a whey culture, you also preserve a reserve culture in the form of yogurt. A portion of this can be frozen and kept for a very long period of time (a few years)
This is important because we work with unpasteurized milk, meaning there are a lot of organisms present to possibly compete with our culture bacteria. If we would just hold over the whey by itself, reason would tell us it would eventually become a different mix of bacteria. But we have 2 ways of getting around that. First, we add a tablespoon or so of our yogurt into every liter of preserved whey. This reintroduces the good bacteria. Second, the whey is heated to a fairly high temperature, which is going to kill off most unwanted organisms but allow the thermos to live on (our cheeses are thermophilic). So our whey culture is reinforced, quickly heated, then quickly cooled and incubated overnight. This keeps our culture going strong.
Also important is that when we make our yogurt, we sterilize the milk as part of the process even if using storebought stuff. This for two reasons, to kill off anything that might compete with our culture, and to break down certain proteins allowing the yogurt to set up thicker (this is nice if you want to eat it)
Also, all culture-handling equipment is repeatedly cleaned and sanitized.
You could use frozen culture to start a new batch, but you would have to go through a multi-step process.
Thaw the culture, slowly warm it up to incubating temp, and leave it alone for a few hours.
You should test you cultures when incubating like this, and they will fall into a fairly narrow acceptable range of acidity (%TA) the specifics will vary with the culture used, and I would give degrees SH which would probably mean nothing to you anyway :/
Sterilize some milk yourself, and flash cool it down to incubating temp with a cold water bath
add the thawed culture stock. This is a very small quantity.
incubate this stuff overnight.
sterilize some more milk, this time a liter or so.
if using a thermo culture, quickly heat the cultured milk to say 150 degrees with a hot water bath, then with a cold water bath back down to incubating temp.
Add cultured milk to sterilized milk.
incubate this overnight.
this should give you a nice, happy thermophilic culture. It will no longer be exactly what you got in the package but that is not necessarily a bad thing. This will yield you a culture more akin to a traditional Old World culture, rather than a laboratory culture. It will have dozens of bacteria growing in it, instead of two or three, but be assured they are good.