An issue was discovered in Singularity 3.1.0 to 3.2.0-rc2, a malicious user with local/network access to the host system (e.g. ssh) could exploit this vulnerability due to insecure permissions allowing a user to edit files within /run/singularity/instances/sing/<user>/<instance>. The manipulation of those files can change the behavior of the starter-suid program when instances are joined resulting in potential privilege escalation on the host.
Sylabs Singularity 3.2.0 through 3.6.2 has Insecure Permissions on temporary directories used in fakeroot or user namespace container execution.