It seems that it's a given that you will not find that substring. The larger it is, the less likely you will find it and the less likely it will repeat in the uncompressed file.
It is very unlikely that the length of the sequence will be smaller than the space required to store X. Your plan is similar to saying "The input could contain long repeated segments containing only zeroes. Compress those using scheme Z. The longer the file, the more likely this is to occur.". Information theory allows us to prove that this cannot always work. In fact it is very unlikely to work for a specific randomly generated target file.
Assuming the target file is competently constructed, the chances of winning wouldn't make it a rational bet for $0.01