Perfect secrecy over Stirling numbers
What, exactly, are your trying to accomplish with this construction?

Yes, you're correct in that, given a sequence of messages $m_0, m_1, m_2, \dotsc$ and a fixed ciphertext $c$ (assumed to be all of the same length), we can easily calculate a sequence of keys $k_i = c \oplus m_i$ such that $k_i \oplus m_i = c$.

However, I don't see any way to get a useful cryptosystem out of this.  If you don't transmit the keys $k_i$ to the recipient, there's no way for them to recover the messages $m_i$ just from $c$; indeed, that would be clearly absurd, since $c$ may be chosen to be completely random and independent of all $m_i$.  Conversely, if you do transmit the keys $k_i$, then the system is easily broken by an adversary who intercepts the "keys" &mdash; it's basically just a many-time pad.

Also note that you can't transmit the keys in advance, since, once $c$ is fixed, each key $k_i$ will depend on the corresponding message $m_i$.  So, unlike a traditional one-time pad, your scheme isn't even good for the "have secure channel now, need to communicate securely later" scenario.