Not at all familiar with LotHS due to my severe GW allergy.

Depending on relative time scale I would say roll a D6:
1 - arrives this turn during movement after all others moved
2-5 - arrives before movement by others next turn
6 - falls/trips on stairs all figures roll a D10 (alternatively lose movement this turn):
1 - jumps over figures/falls forward near top of stairs, rolls, stand up at end of movement phase
2-4 - try again next turn, following figures not affected
5-8 - blocks passage/stairs for all following figures this turn, all try again next turn
9 - wounded (if no wounds in game, treat as 5-8)
10 - fatal accident figure dies.
Gracias,
Glenn
who just committed an act of over science of an answer