As far as I'm aware, that is only true for L1, not H1B, which has a 60 days grace period. I don't know how it affects folks with AOS to an I-485, though.
L1 - if you lose your job and you have no other status (ie have not filed for green card or have your H1B), that's it. You have to leave within 60 days and you cannot work at another company in the US.
H1B - you can switch to a new company and they port your H1B with USCIS. Otherwise, 60 day grace period to leave.
Adjustment of Status to 485 - if it has been pending with USCIS for more than 180 days & you have your EAD, you can port to another company under the AC-21 act.