Aside from nouns, na adjectives such as 好き may potentially be accented on their final mora (e.g. [好きな]{LHL}, OJAD).
Verbs and i-adjectives show limited accentuation options. Timothy Vance’s descriptions of the accentuation patterns of various inflected forms in The Sounds of Japanese (2008) appear consistent with a generalization that the forms of verbs and i-adjectives never have an underlying accent on the final mora, although I didn’t see an explicit statement to this effect.
Per Vance, there are a few situations where a verb or adjective form may receive an accent on the final mora when followed by another word, but there is no contrast here between underlyingly accented and unaccented lexemes. Vance describes it in terms of adding an accent to the last syllable of an unaccented verb or adjective form in the following circumstances:
The gerund of an unaccented verb gains an accent on the last syllable when followed by /wa/ or /mo/, as in /maketeꜜwa/ and /maketeꜜmo/. (Vance, pages 168-169)
When the dictionary form of an adjective is followed by です (forming the polite nonpast affirmative) or by the pronoun/nominalizer の, an accent is placed on the final syllable of the dictionary form. For nearly all adjectives, the final syllable of this form contains a diphthong (/ai/, /oi/, /ui/) or the long vowel /ii/, in which case the accent falls on the second-to-last mora: /aꜜi/, /oꜜi/, /uꜜi/, /iꜜi/. (In Tokyo Japanese, it's normally impossible for an accent to be placed on the second mora of a long vowel or of a diphthong.) But 遠いです and 遠いの are pronounced as /tooiꜜdesu/, /tooiꜜno/ with an accent on the final mora, suggesting 遠い is here syllabified as /too.i/. (Vance, pages 178-179) Interestingly, OJAD displays the alternative accentuations /tooꜜidesu/ and /toꜜoidesu/ for 遠いです; I don't know any more about this.
See also In what cases do 平板 verbs change their pitch? and Pitch accent of nominalizers
One exception is accented verbs like 吹く where the second-to-last mora has a devoiced vowel; some speakers reportedly shift the accent onto the following, final mora. As far as I know, there is no verb where shifting the accent from the second-to-last mora to the last mora is obligatory.
I'm only an occasional learner so cannot offer much practical advice.