For example, the language might be such that a a stage-level adjective like "available" would agree in predicative position, but an individual-level adjective like "intelligent" would not.
Russian is such a language, although this feature is not followed by speakers as consistently as, for example, in Spanish.
The majority of the Russian qualitative adjectives have two forms, short and full, the short one being the oldest, Proto-Slavic had only short adjectives, and the full adjectives were formed from the short ones, by adding article-like demonstrative/3rd person pronouns as suffixes to the short form of adjectives. Short forms can function only as predicates, full forms can be both predicates and attributes:
Short forms: болен (masc.), больна (fem.), больно (neut.), больны (pl.)
Full forms: больной (masc.), больная (fem.), больное (neut.), больные (pl.)
Both forms can function as predicates, but when the predicate is stage-level, a short form is supposed to be used. When it's individual-level, one is to use a full form adjective.
Их ребёнок здоровый. "Their child is healthy." (full form, permanent quality, the child has good health)
Их ребёнок здоров, лекарство ему помогло. "Their child is healthy now, the medicine has helped him." (short form, "right now", the child was sick, but now he's OK)
One more example:
Это платье короткое. "This dress is short." (full form, permanent quality, the length of the dress is physically short, I have longer ones for more official events)
Это платье мне коротко, а тебе будет в самый раз. "This dress is short for me, but it'll fit you perfectly." (short form, "only for me", the length of the dress is normal, only I don't like it, it's not for me)
This distinction is slowly but steadily getting lost, more and more speakers would use full forms in all the situations or use now the full and now the short form in the same context, for some adjectives the full forms are never used, with some adjectives the two forms came to mean so different qualities that they are now perceived as two different adjectives. To put it short, this system is decaying. Still it's not dead yet which adds one more nice challenge for learners of Russian.