Does illegal immigrants can pay solicitors and stay in England even though they have been caught by a police?

My bf is from Kosovo, and I'm wandering if its true that he paid a solicitor to stay in UK. He's swearing that he has paid a solicitor 4 000 pounds after police had caught him with out any doents, pport or ID. Is it possible to deal with that so easily, to stay in England with out any paper even though police knows that he is here illegal?