This is the actual text of the law:
"Every alien, eighteen years of age and over, shall at all times carry with him and have in his personal possession any certificate of alien registration or alien registration receipt card issued to him pursuant to subsection (d). Any alien who fails to comply with the provisions of this subsection shall be guilty of a misdemeanor and shall upon conviction for each offense be fined not to exceed $100 or be imprisoned not more than thirty days, or both."
If you live near a border where they frequently have those raids and checkpoints, then you probably have a higher chance of having to show the card while going about your daily business than having the card stolen. But outside of those areas, it's far more likely you'll get robbed than having to show proof of legal status. And if you get robbed and lose both your DL and GC, your life becomes like hell when you try to replace them.