ElGamal proxy re-encryption
Disclaimer: The use cases for proxy re-encryption are very specific. From your description it is not clear to me why you don't just encrypt the message with a different key for your someone.

Looking at the scheme it seems to me that someone only gets $x_2$ and cannot use that to learn anything about $x_1$. Even given multiple pairs $x = x_1^{(i)} + x_2^{(i)}$; if only the $x_2^{(i)}$ are known any $x'$ could be the correct key for $x_1^{(i)} = x' - x_2^{(i)}$.