A sentence like 我喜欢的人是小明。What is the role of the shi and de in this sentence? Would the shi be considered a copula? And is the de a possessive marker?
This is not a 是……的 construction, and you can tell because the 的 comes before the 是.
他 是 小明。
He is Xiao Ming.
我喜欢的人 是 小明。
The person I like is Xiao Ming.
Here the 的 lets us know that 我喜欢 = "I like" is being used as an adjective, so 我喜欢的人 = "the person I like".
Another way to use 的 (de) is as an attributive. It's just a way of connecting adjectives or other words with a noun. It gives us more information about the noun, and the 的 (de) makes it clear that the extra information is connected to the noun.
Structural particle "de", Chinese Grammar Wiki
Whether or not you consider this 的 as a "possessive particle" seems to be a matter of linguistic preference. It seems the copula in this sentence is 是.
"是" is considerd to be a copula, while "的" is not a possessive maker but just part of the adjective "喜欢的".
The sentence should be translated into English as "The person I like is Xiao Ming". However the sentence pattern is closer to "My favorite person is Xiao Ming". It's obvious that "favorite" is an adjective here, equivalent to the role of "喜欢的".