1. To continue to be physically beneath something or some surface. I remained under the blankets until the scary noises in the house went away. You can't remain under the ice of a frozen lake for more than a few of minutes without getting hypothermia. The dog always remained under the table throughout the meal in hopes of getting a few scraps.

2. To continue to be unconscious, especially when it has been medically induced, as by anesthetic. In this usage, no noun or pronoun comes after "under." The vast majority of patients remain under throughout the entirety of their surgery, though it is technically possible to wake up in the middle of it. How long do you expect her to remain under, Doc?

3. To continue to be subject to someone's authority, rule, or control. We've remained under this dictatorship for the last 60 years—it's all we know. I remained under the senator even when I disagreed with her policies.

4. To continue to be subject to some ongoing conditions or circumstances. The CEO will remain under investigation his involvement with the company's illegal activity can be determined. She remained under house arrest for nearly two years.

5. To continue to be undergoing or receiving some the effects of some ongoing process. I'd like the patient to remain under observation for a few more days. She must remain under constant care until the wound is healed.