Hoffman's Isocyanide test: How does addition of concentrated HCl degrade the isocyanide formed?

Isocyanide is not as toxic as its isomer cyanide and can be tolerated. The purpose of its removal is due to its disagreeable odor which is not at all tolerable.

While some isocyanides (e.g., cyclohexyl isocyanide) are toxic, others "exhibit no appreciable toxicity for mammals". Referring to ethyl isocyanide, toxicological studies in the 1960s at Bayer showed that "oral and subcutaneous doses of 500-5000 mg/kg can be tolerated by mice".(Wikipedia)

Isocyanide is removed on the basis of its property of acidic hydrolysis.

Isocyanides are stable to strong base (they are often made under strongly basic conditions), but they are sensitive to acid. In the presence of aqueous acid, isocyanides hydrolyse to the corresponding formamides:

$$\ce{RNC + H2O → RN(H)C(O)H}$$

This reaction is used to destroy odorous isocyanide mixtures. Some isocyanides can polymerize in the presence of Lewis and Bronsted acids.

But the story does not here. The formamides are still pretty unstable and further degrades to form amines and formic acid in the presence of acidic medium.(Here)

Isocyanides are hydrolyzed by dilute mineral acids to give primary amine and formic acid (Isocyanides are not hydrolyzed by bases). Isocyanides are hydrolysed only by acids and not alkalies because the negative charge present on carbon atom in isocyanides initially attracts electrophiles ($\ce{H+}$) but repels nucleophiles ($\ce{OH–}$). When a proton gets attracted to negatively charged carbon atom, the tendency of this carbon atom to attract a nucleophile increases due to presence of positive charge on the N atom and hydrolysis is facilitated as shown below:

Mechanism:

Here is a research paper for a reference.