Thu Apr 23, 2020 11:13 am by 6275LA
Yes, certainly possible.
Although having a locked padlock stolen by cutting it is not entirely preventable, some large institutions (hospitals, universities, etc) do take measures to prevent cylinders from leaving their control. For example, a university has an off-campus building no longer needed and will sell it. Before putting it on the market, the campus lock shop will strip all interior doors of their cylinders (they can leave the rest of the hardware on if they so desire) and all exterior doors will get replacement cylinders (usually aftermarket SC4 or Y2) for temporary security when the building is sold. Then it is the responsibility of the new owner to decide what to do.
I have heard of a university campus (I don't remember where) that had all doors that are normally unlocked (such as rest rooms and dorm living rooms) keyed alike, off master. That way, because stealing cylinders on open doors is easy, if one were stolen it would not lead to making a master key.