Peter Weiner, who first invented suffix trees gave an answer to this question on p.3 of "Linear Pattern Matching Algorithms"[1]: "If P does match a substring of S, then reverse(P) also matches a substring of reverse(S). This observation implies that every technique which solves a pattern matching problem working from left to right has a dual procedure which works from right to left. In what follows, we adopt a left to right view point, referring only briefly to dual concepts as appropriate."

[1]https://pdfs.semanticscholar.org/d339/0f13eed511cde1116446e7...