You can mine for a public key to have a certain pattern. Essentially going through a bunch of private keys until you land a public key that meets your criteria.
Discussion
Yes, like a vanity PubKey. But as soon as you want to find private keys that gives more than 8-10 said letters/numbers, it become impossible due to the extreme computing power needed.
Finding anothers accounts private key by generating priv/pub keys until you find it, is impossible in all reality.