Ah, the beauty of selective quoting
Actually, the law says that you have to carry it with you
and in your personal possession at all times.
INA 264(e):
"(e) 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."
Here in LA, and in Arizona, they can.
And a "certificate of registration", if you are not a US citizen. Google for the Texas Raid of 2000, if you want to know what can happen if you don't have it with you (here's a hint: arrest...)
Here is a quote from one of the sites:
"Since most programmers pleaded that they kept their important documents at home or in bank vaults, they were escorted to their residences or banking institutions. At the residences, they were escorted under armed guard in handcuffs in front of their neighbors. The officers would conduct searches of the apartment for hidden persons and/or firearms. These searches occurred without a warrant or permission of the resident. Even after producing original work visas and passports, many were taken to an INS detention facility."
You always have to carry it with you, according to law.
Oh, this old strawman again. Are you losing stuff all the time???