Nouns, pronouns, and verbs can serve as subjects.
(noun) The dog ate the cake.
(pronoun) She died after the meal.
(verb, gerund) Eating the cake led to her death.
(verb, infinitive) To eat the cake was a risky move.
For verbs, present participles (often defined as gerunds) or infinitives serve as subjects. (The Critical Reader chooses to specify these in their answer for "What parts of speech can be subjects?") The colloquial explanation, represented in places like ThoughtCo, is that the gerund or infinitive is a verb that serves as a noun phrase, which allows it in turn to serve as a subject.
Other parts of speech are trickier. In general, the words will serve as a noun or noun phrase, most likely due to a process of nominalization or due to an implied noun phrase serving as subject. Note: you want to be deliberate about what you are doing and how the nominalization will be understood; you cannot slap any adjective at the start of any verb and say, "That's my subject."
First, implied noun phrases. Take these examples:
(adjective) Slow and steady wins the race. (Source: idiom)
(adjective) Rare is fine. (Source: Cowboy's Mail Order Bride)
These adjectives have an implied noun phrase that is the subject; they have entered such wide usage that the noun need not be specified. (Examples: slow and steady pacing OR slow and steady action; rare steak.) Context or idiomatic usage suggests how the adjective should be understood.
There are also adjectives and (occasionally) other parts of speech that can be nominalized, or made into nouns:
(nominal adjective / adjective turned into noun) The rich get richer and the poor get poorer.
(nominalized preposition) For is used to specify who will receive the gift card.
Usually these forms are treated as nouns.
Finally, and especially with linking verbs, it is possible to move the grammatical subject to the end of the sentence.
Red is the color of my car.
The subject has been moved to the back of the sentence, and another element has been moved to the front (ThoughtCo gives many examples of subject inversion and fronting). The subject is still the color of my car.