My last sentence missed out a crucial stage in deriving a reversible pair from 651.
651/2 = 325.5 as I said, then reverse and add that result once to get 331.023. Add that to its reverse, and you get back not exactly to 651 but to 651.156, which I'm suggesting is an acceptable approximation. So 331.023 and 320.133 is the reversible pair I got by decomposition from 651.
There are plenty of similar examples, in four digit numbers as well.
Another clarification, by "know in advance" I meant is there way of deciding in advance whether or not a given three digit number has a solution before starting the procedure you describe?