Would sodium salicylate dissolve in HCl?
HCl is in almost all cases already aqueous for common chemistry, mostly dissociated into $\ce{H^+} + \ce{Cl^-}$ because it is a strong acid, which means water is the primary solvent, not HCl. Pure HCl under ambient conditions is actually a gas (thus certainly not a pure liquid solvent).

That leaves the compound in question insoluble in the water after being protonated by $\ce{H^+}$ to form the insoluble acid molecule.

The process I mentioned in the comment is illustrated here: