Branding also reduces the escape chance and increases jail effectiveness. Higher grade slaves will have longer rebellion strength and generally be more likely to escape. At game start the jail is barely fit for purpose and it isn't until you get a number of upgrades, such as branding, that jail becomes effective. I'd advise newcomers to jail only slave grade and poor grade captives until you are more confident in how the jail works.
Escapees are essentially gone. I think there is some specific Emily escape content but I've no idea if it is related to the jail at all. Unique characters generally have no protection from escape or death.
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Now that you mention it, branding did say that there would be a chance that they'd be returned to you if escaped? Idk. But yeah, it does make it harder on the premise that they will be treated criminals and looked down upon as far as in-game narrative goes.
As for Emily's escape sequence, mmm...I wonder. For now, I try to avoid her on the premise of role playing as a start up aspiring magician that had studied for years, though with little luck until the big break of getting the mansion whilst meeting a dependable stranger and partner on the way.
No protection eh, oof. Protect them all, one way or the other. Thanks for the head's up.