Pids do wrap and do eventually get reused. However, pids assigned to recently running processes are not soon reused.
so, in practice the problem you're worried about never happens.
It is theoretically possible as far as I can tell.
However, that would mean that
pkill was running slow enough that a whole bunch of new process IDs could get allocated between finding the process and killing it
the rest of the system was running fast enough to create all those processes and get to a point where the recently used pid was freed.
As pointed out in comments, either you are root or the process is running as the same user
It's possible there is some way of attacking pkill so it's that slow, but such an attack would almost certainly be a kernel bug.
I've never been in a situation where worrying about this problem was the right design decision.
Pids do wrap and do eventually get reused. However, pids assigned to recently running processes are not soon reused. so, in practice the problem you're worried about never happens. It is theoretically possible as far as I can tell. However, that would mean that
It's possible there is some way of attacking pkill so it's that slow, but such an attack would almost certainly be a kernel bug. I've never been in a situation where worrying about this problem was the right design decision.