Final answer:
The organism described is Cryptococcus neoformans, an encapsulated yeast detectable by negative staining techniques and associated with infections in immunocompromised people.
Step-by-step explanation:
The organism described as narrow-based budding yeast cells that show a bright red capsule with mucicarmine or periodic acid-Schiff staining is Cryptococcus neoformans. This encapsulated yeast can be identified using negative staining techniques such as India ink, which leaves a clear halo around the cells due to the presence of the capsule. A characteristic of Cryptococcus neoformans is its ability to cause opportunistic infections, particularly in immunocompromised individuals, such as those with AIDS, leading to conditions like cryptococcal meningitis.