It isn't as if they're pinged the day it happens, and depending on the individual may take some time to reclaim the watch for the next person who arrives -- as such, the longest a character may keep hold on a dropped character's watch is a week before someone realizes their regular isn't about anymore, and the watch will also stop functioning about the same time as the latent magic connected to the watch disappears.
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It isn't as if they're pinged the day it happens, and depending on the individual may take some time to reclaim the watch for the next person who arrives -- as such, the longest a character may keep hold on a dropped character's watch is a week before someone realizes their regular isn't about anymore, and the watch will also stop functioning about the same time as the latent magic connected to the watch disappears.