For examples here I'll use cases. However, this applies to any prevalent morphological thing - tense, aspect, volitionality, evidentiality, number, etc - it's just a question of finding a way of applying it.
Now, sometimes, sound changes happen at boundaries of words. An example of this is how the former Finnic accusative case suffix -m has merged with the genitive case -n, due to a sound change that turned all final -m into -n, including stem-final -m. Thus, some words whose nominative form ends in -n have inflected forms with an -m- instead: sydän, sydämen. Historically, there's probably also been a form sydämem, which now comes out as sydämen as well.
Beyond cases, a language can have other affixes, e.g. possessive affixes, various clitics, etc. We can now imagine a situation where a different affix blocks a merger of cases by means of having had a different sound change induced (or just plain prevented it), a case distinction can survive in a limited environment, such as, say, before something analogous to Latin -que and similar. Finnish has -kin serving a similar role as -que, and we can imagine then a different version of Finnish having a change -mk- > -mp-. Then, we'd have a situation where 'a heart (nominative) too' would be 'sydämpin', 'a heart's too' would be 'sydämenkin' and 'a heart (acc) too' 'sydämempin'. The negative version of 'too', -kaan ('not even', 'not ... either', 'neither a/the ...'
Now, as I mentioned, this needn't be a case - could be a volition marker or whatever.
Describing such morphological quirks in tabular form requires some special notation, e.g. some kind of diacritic that serves exclusively to mark the existence of an underlying phoneme that may resurface. For the faux-Finnish example, we can consider m̄ for this role. Now, we could get the following pattern for the word sydäm̄:
case underlying form realization nom: sydäm̄ sydän acc: sydäm̄em̄ sydämen acc, clitic kin: sydäm̄em̄kin sydämempin gen: sydäm̄en sydämen gen, clitic: sydäm̄enkin sydämenkin
The thing I find relevant or interesting here is really the distribution of mergers vs. distinction. However, a convenient and succinct way of encoding such things in a morphological table is obviously relevant for descriptive purposes. The approach given above - using arbitrarily redefined diacritics - seems to have one great disadvantage: the requirement of learning to mentally apply the sign. In a short description, this is surprisingly taxing. If you've devoted your life to study a particular language, it is no big deal, but in a text you barely read once, it is a bit taxing. Another method that would require a bit more awkward writing, but be more parseable could be something like the following:
Essentially replacing m̄ by mm > n / _# throughout the dictionary. Of course, for this use, I assume a really short sample dictionary in a fairly short text.lexical example: sydämm > n / _#morphological example: -emm > n / _#
This could be expanded into marking relevant sound changes wherever they apply in morphophonological contexts.