Garfield's rise was similar to Polk's in 1844. It couldn't happen today. Certainly not with Paul Ryan. A presidential candidate has to have some kind of personal appeal or pull. He or she can't simply be somebody pushed by the party machine into the race in the middle of it.
Under Rule 40, it must be a current candidate. And I suppose this would include those who may have “suspended” their campaign but remain candidates. If they change Rule 40 before the convention, then watch out.