While bulbs die off in nature and aren't removed, whole plants also die in nature if they get a disease or start to rot. If you care about loosing the plant then removing the bulb is the best thing
Was the brown pbulb soft and mushy or was it just drying up? I reread your original post and you didn't say it was soft and mushy, you just called it a yuck bulb. If it was mushy and soft, I think it needed to be removed. If the pbulb was just drying up, then I would have left it until the plant grew a couple new growths.