This question discusses the acid and base species that are found in an alkaline buffer, not the species that are required to produce an alkaline buffer. In other words, the buffer already exists at equilibrium.

Let's look at the dissociation of a common weak acid, acetic acid, to help answer this question:

Acetic acid is defined as a weak acid because it partially dissociates in water to form its conjugate base, acetate. Similarly, acetate is defined as a weak base because it partially dissociates in water to form its conjugate acid, acetic acid. Thus, if we were to add pure acetic acid or acetate salt to a solution of water, a small amount of the conjugate species would form. In short, the conjugate base of a weak acid is a weak base, and vice versa.

When both a weak acid and weak base are present in a solution, one species will be stronger in magnitude. The stronger species will "win" and make the solution either more acidic (acidic buffer) or basic (alkaline buffer). We typically describe the stronger of these two species to be the weak acid/base, and the weaker species to be the conjugate. This is why we do not typically say alkaline buffers are made from reacting a strong base and a weak acid (in a 2:1 ratio). Instead, we say alkaline buffers are made from reacting a strong base with the conjugate acid of a weak base (in a 2:1 ratio).

To conclude:

*Note: The conjugate base of a strong acid is sometimes called a weak base, and the conjugate acid of a strong base is sometimes called a weak acid. However, these weak acid/base conjugates are so weak that they are practically inert (i.e. very weak). Thus, they can't be used to form buffers at all. For example, chloride (Cl-) is the conjugate base of hydrochloric acid (HCl), which is a common strong acid. However, if we were to dissolve table salt (NaCl) into water, this solution would be neutral, not basic. Thus, Cl- is a very weak base and could not be used to form a buffer.

A strong acid (e.g. HClO4) and its conjugate base will not form a buffer. However, a buffer can be formed using a strong acid and the conjugate base of a weak acid (in a 1:2 ratio).

For example, HF is a weak acid, and its conjugate base (F-) can form a buffer when a strong acid (e.g. HCl) is added. This strong acid completely dissociates to form H+ ions, which will react with F- to produce HF. Since the ratio of strong acid to weak base was 1:2, 1 part HF will be formed from this reaction and 1 part F- will remain unreacted. These 2 species will constitute the buffer.

Recall that the stronger an acid, the weaker its conjugate base. In the case of strong acids, their conjugate bases are so weak that they are functionally inert. Since HClO4 is a strong acid, this makes ClO4- neutral. These species will not form a buffer. To make a buffer, a different conjugate base would be needed (not ClO4-), corresponding to a weak acid.

​