In general, DoS attacks are only designed to cause (as their name suggests) a denial of service, i.e. a compromise of the availability of the service.
Other forms of DoS, e.g. triggering a null pointer dereference, might be used to compromise integrity by crashing a service without it having time to cleanly close files, leading to data corruption (loss of integrity). Databases are an obvious target for that kind of thing.
Firewalls and other security services should fail closed if they are effectively DoS'ed. I'm not aware of any case where something like that would fail open. However, I could foresee a scenario where a server behind a load balancer falls to a DoS attack, so the load balancer shifts to a secondary system, which is configured in a weaker manner, thus revealing that vulnerability externally.
Outside the CIA triad, you might find that DoS attacks are used to divert attention and staff resources away from a more subtle attack.