Perhaps instead of immediate HFS beyond the caverns...
There could be sprawling ruins, destroyed cities of a civilization of the past. They'd be full of dangerous traps, hidden traps, but the city would have rooms, doors, structures for you to use. Possibly fresh water. They could also have various 'corrupted' versions of cave creatures, trolls with twisted arms of lead, crundles with steel horns, etc.
"The miners report sightings of ancient engravings in the depths."
There could be entire cities of animal men, gathered around a pillar of gold/platinum/adamantine/shiny they worship as a god, or somesuch. They see your intrusion as sacrilege, and would immediately attack any dwarves they see within the city limits.
"The wall crumbles away, revealing a huge cavern with a pillar of gold at the center. Many animal people surround it, as if they worship it, and they seem offended by your intrusion."
There could be ancient burial grounds, and disturbing them triggers a zombie attack.
"A thick fog covers this small cave. You can barely make out mounds of dirt with slabs rising out of them through the fog."
"Terrifying moans! The dead have risen!"
There could be a temple to an ancient god, and destroying part of it brings a punishment of some sort apon your dwarves. Could vary from a plague, a famine, drought, heat wave, blizzard, etc. The god could still be alive, and make demands of your dwarves like a noble.
"Your miners have discovered a very old structure in the depths. It has many stained glass windows, and you can hear ominous chanting coming from within."
Of course, these are only ideas.