There's a reason I pick up my refills exactly on time, even if I still have some of the old prescription left. That little overlapping buffer gives me great peace of mind.
Recently, my wife was going to be out of the country about a week-and-a-half. Her prescription for a medicine to manage arthritis would run out at the very beginning of that time. But insurance company policies refused to allow her to fill it even a little bit early. As a result, her only option was to go without the medicine for several days.
Policies should be set by organizations whose primary goal is to provide effective health solutions, not organizations whose primary goal is to minimize costs in order to make a profit.
She could've gone to her provider to discuss adverse side effects. Sometimes they will prescribe a new medication that could be filled immediately.
She could've got a pill cutter and cut the tablets in half, or space out the doses, or otherwise take less than the specified dose for a few weeks.
She could've asked the pharmacist about OTC treatments which could be safely substituted during the gap time.
She could've gone to the emergency room or urgent care in the destination country, and tell the provider "I have run out of medication!" This would be covered by the traveller's insurance that you purchased for the trip.
The idea of someone cutting pills in half because their insurer is reporting record profits drives me nuts.