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I've read that $\ce{HCl}$ acts as a weak base in $\ce{HF}$ solvent, which means $\ce{HCl}$ is supposed to lose $\ce{H+}$ ion to $\ce{HF}$. $\ce{HF}$ is a weak acid compared to $\ce{HCl}$, then shouldn't $\ce{HF}$ be accepting the proton and HCl be losing it. Why doesn't this happen?

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As Poutnik hints in his reference, it is not accurate to call $\ce{HF}$ a weak acid in water. What appears in dilute aqueous solution as a weak acid is the hydrogen-bonded ion pair $\ce{H3O^+F^-}$ that forms when $\ce{HF}$ reacts with water. If this ion pair is placed in concentrated $\ce{HF}$, it will act as a strong base, forming $\ce{H3O^+}$ and $\ce{FHF^-}$ where the latter is the characteristics basic species in $\ce{HF}$. Thus $\ce{HCl}$ is a stronger acid than the aqueous $\ce{H3O^+F^-}$ solute in water, and $\ce{HCl}$ is also less basic than $\ce{H3O^+F^-}$ in $\ce{HF}$.

The Hammett acidity function of neat $\ce{HF}$, unsullied by water, is close to that of 100% $\ce{H2SO4}$. So, anything with appreciable acidity in $\ce{HF}$ would cross over into superacidity. $\ce{HCl}$ does not make it.

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    $\begingroup$ Note that the Hammer function of liquid HF is comparable to the value of H2SO4. $\endgroup$
    – Poutnik
    Jun 27 at 11:02
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    $\begingroup$ So is the Hammett function. Autocorrect got you maybe? $\endgroup$ Jun 27 at 11:16
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    $\begingroup$ :-) Definitely. Google knows better than you what want to say. :-D $\endgroup$
    – Poutnik
    Jun 27 at 11:19

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