Parallels Desktop runs prl_disp_service as root. Local clients reach it on the world-writable socket /var/run/prl_disp_service.socket. PrlSrv_LoginLocal accepts peer credentials. No Parallels signature. No admin group.
After login, PrlSrv_InstallAppliance lets you pick the appliance folder (sVmParentPath). The daemon unpacks with one string, tar -xf "%1" -C "%2", then Qt QProcess::splitCommand chops that string into words. A quote in the folder name closes early. The leftover text becomes extra tar flags. macOS tar --use-compress-program= runs the named program as root.
JFrog has a private proof of concept that obtains root on Parallels Desktop 26.4.0. The same proof of concept does not obtain root on 27.0.1. Public exploit details are not included in this record.
Upgrade to Parallels Desktop 27.0.1 or later.