Either print and carry the I-94 around with you, or save the PDF of it to your phone (and hope you have battery life if you ever get stopped by these people).
If you're a citizen, my understanding is that you only have to show some form of ID (e.g. a driver's license).
https://www.dallasnews.com/news/immigration/2019/07/22/dalla...
so it sucks he stayed there so long but are you gonna say this is normal? can you find any case where a legal person with no false papers or illegal family members while crossing the border got detained?
That seems... foolish? Like allowing a root/intermediate CA to sign leaf certs to be valid after their own expiration.
The point is that you must have clear legal status and documentation, whether that's physically on you as a person (for green card holders) or available to be looked up (for everyone).
All of this relies on a judgement call by ICE, and many people do not trust their judgements. Not unjustifiably.