Try a billion times to form the next block, and whichever copy succeeds thats cool, all the copies that failed cost you no coins they are in effect just a kind of hashing, a doing of work, the more different attempts you make to form the next block the greater your chance of doing so, while it costs you no additional stake since all the copies are all using the same stake. Its only the one that actually gets lucky and finds a block that anyone else sees.
No, that's not how POS works. Some early POS coins may have had bugs that allowed you to do something similar to that, but nowadays that's not possible. If you try a billion times in parallel with the same stake, you either fail a billion times or succeed a billion times (a billion successes all in the same block, so they are as useful as only one - ie you find the exact same block a billion times).
There are two problems with POS that I'd care about, and I think both have been called "nothing at stake" at least once, but they are different issues:
- One is that in POW finding a block or not depends on the (hash of the) transactions of the new block. But in POS, once you find a block you can create another one (at the same height) with different tx's for free.
- The other one is a history rewrite: in POW, if I own in the present 51% of the hashrate of some point in the past, I can do nothing with that. For example you can buy some ASIC that has more hashrate than all the network combined had in some moment of 2011. But that's useless. However in POS if I have control in the present of the private keys to a stake larger than 51% in some past then I can use that to rewrite the blockchain from that time until the present (overriding the tx's in which that 51% changed hands).
Many coins take measures to mitigate -with different levels of success- the consecuences of these two problems. However it's hard to deny that they are security weaknesses inherent to POS.