In DSA, the value of $r$ is generated as:
$r = (g^k \bmod p) \bmod q$
ECDSA is similar, using the $x$ coordinate of the generator $g$ scalar-multiplied by $k$, again taken modulo $q$.
It's well-known, particularly by Sony, that $k$ must be different for each message signed, or the private key leaks.
Due to the construction, it is possible, but unlikely, to generate two different $k$ values that result in the same $r$ value. If you happen to generate two signatures of different messages that have the same $r$ value but different $k$ values, does it break security?