Banks often ask for personal guarantees from ltd owners for precisely this reason. I've just skimmed the T&Cs and I can't
see any indemnity clauses, but that document's massive and I'm just some guy, so who knows.
(Incidentally, it's fairly common to structure a pair of ltds with the assets in one and the liabilities in another. If the whole thing crashes and burns, at least the IP doesn't go with it).