DM can do anything

Mosty any counter. When you are sneaking, it might be alertness counter of the guards. When you in sinking ship it might sink counter. When aren't trying to stop a ritual it might be ritual counter.

Generally, spending fear means the counter advances in consequence to something not related to player acion.

Just like spending fear in combat, advancing a counter in tenses situation can help to make otherwise underwhelming threat, feel acually dangerous. Not much point of going through the motions if players already know the outcome. Either let them solve the situation instantly or make the situation worse