Briton Riviere's 1875 painting "All That Was Left of the Homeward Bound" is described by the British Museum as depicting "A little girl, cradling a little dog on her chest, lying asleep, bound to the mast of a wrecked ship, floating on the open sea."
Is the painting meant to be showing a little girl who was bound to the mast as some form of punishment/captivity prior to shipwreck?
Or did they bind small or vulnerable people to the ship during bad storms so they wouldn't be tossed about?
Or is there evidence that they used to bind vulnerable people to the mast when a shipwreck was inevitable in the hopes they would stay afloat past the point that they could hold on under their own strength, in the hopes they might be rescued?
Link to the painting: https://www.artrenewal.org/artworks/all-that-was-left-of-the-homeward-bound/briton-riviere/20970
Link to the British Museum description: https://research.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=1621895&page=1&partId=1&peoA=106686-2-60&people=106686
While I can't specifically speak to the era you're interested in and look forward to some of the folks familiar with that timeframe responding, modern day sea services specifically require watchstanders even in the heaviest of conditions if safety demands it. While the preference is to keep them inside if possible, if you need someone on the deck to see where you're going, then it would be considered negligent to not have them outside - and also negligent not to rig them to the superstructure so they don't go overboard in the process. Indeed, I've seen pictures taken by someone who got to do exactly that in a hurricane. They were given a sound-powered phone and quite literally lashed up to the electronics mast on the weather deck for a two hour watch to let the bridge know if they saw anything in ~100 mph gusts and 40 foot seas. They were crazy (the pictures, but I suppose you could say that about the watchstander too.)
So in the age of sail, I have no doubt the same rules and safety measures applied to watchstanding, especially prior to the advent of radar and night vision when you'd have people up in the crows nest at the top of masts.
But to your last question, yes, in the event of a wreck, even today you'd try to rig someone to flotsam especially if they couldn't swim, so your last guess strikes me as most likely.