Are the page tables of the process preempted swapped out if there is a dearth of memory for new process

Suppose process A has been preempted to allow process B to run. If system memory is low and the kernel needs to reclaim memory for process B, is it possible for the page tables of process A to be swapped out to disk? I understand that when a page belonging to a process is swapped out, the corresponding page table entry (PTE) must be updated to indicate that the page has been swapped. But if the page tables of process A were already swapped out before its pages are selected for swapping, how does the kernel update the PTEs to reflect this? In such a scenario, will the kernel swap the page tables of process A back into memory just to update the PTEs? Or is there some alternative mechanism used? Just tried reading other sources from the internet, didn't find much