Idea: Hungry Space Anomaly
A harmonic, unstable, neutralizable gravitational anomaly (HUNGA) has materialized somewhere near the station. Science has to scan the HUNGA to determine what it wants to eat ("stabilizing items" that match its harmonic frequency). The list of objects it wants to eat is random, and can include foods/dishes/plants, liquids/chemicals, tech-gated objects, unique books (i.e. can't use the same book twice), large quantities of a particular mineral/alloy, rare organs or large numbers of common organs, animals (living or dead), etc.
The HUNGA grows over time. Feeding the black hole stabilizing items will shrink it, stop it from growing, and potentially even permanently neutralize it. Feeding the HUNGA non-stabilizing items or ignoring it for a long enough time will allow it to grow, potentially getting large enough to damage the station and eventually becoming a singulo that will ravage the station.
To fulfill the station objective, you must neutralize the HUNGA by dumping enough stabilizing items inside. To speed up delivery, crewmembers are encouraged to build a disposal or conveyor system to rapidly deliver stabilizing items to the HUNGA, though such a system would need to be guarded by security to prevent sabotage.
If the crew fails to stabilize the HUNGA, the station fails the objective. If the HUNGA grows into a singulo before the emergency shuttle leaves, the station critically fails the objective.
Regarding timescale, it is unlikely that the HUNGA will grow into a singulo over the course of a normal round without someone deliberately throwing mass into the it. However, on particularly long rounds it is possible that a singulo will form. To prevent situations where an empty station is held hostage by a runaway HUNGA singulo, Centcomm has set up an automatic signaller that automatically calls the shuttle when the singulo is formed- albeit a crappy one that only has room for the most expensive to replace crewmembers.
TL;DR - Command receives word of a black hole, crew finds the black hole and scans it, scavenger hunt for black hole food ensues