Answer: The growth habit you describe sounds like cordyline or dracaena. The plant does lose its lower leaves and develops a bare trunk. You can cut the plant at any height and new foliage will grow just beneath the cut. You can also root the top of the plant in water or in moistened soil. What you have read is true.
These plants will grow in low to bright light, in moist to dry soil. The browing leaves can indicate dry air (from air conditioning, perhaps?) or the plant is in a draft. Move your plant, water when the soil is dry and it should perk up.
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