Yes, but there is usually an additional system like Toyota's Safety Stop which WILL detect a stationary object and kick in at the last minute to reduce speed by N MPH before collision.
AFAIK Tesla used to have that via its RADAR but because the new production has no RADAR, new cars can't have it, and they disabled it on the older cars too, in the interest of using a single software version.
At least this is what I've gathered from reading here and elsewhere.
Radar is useless for detecting stationary objects because of far too many false positives. Radar is the reason why these warnings exist. It is not the solution.
Teslas continue to have forward collision warning and automatic emergency braking as standard features whether or not they have radar. But again, they do not detect 100% of all stationary objects and neither does any other automaker's system.
AFAIK Tesla used to have that via its RADAR but because the new production has no RADAR, new cars can't have it, and they disabled it on the older cars too, in the interest of using a single software version.
At least this is what I've gathered from reading here and elsewhere.