Personally Guaranteeing Loan for LLC Issue??

[Devon Angle]

I ran across something that caught my attention that had to do with getting a mortgage for an LLC. Say if the only way to get a bank to loan to the LLC that holds the rental property was to personally guarantee the loan, does that break the protection of the LLC say if it was sued by a tenet for getting injured. Like what if the Insurance policy isn't enough to cover the damages, can the tenet then go after the owner of the LLC personally since they guaranteed the loan with their own finances if the LLC couldn't make the payments??