I live in a community property state, all of my accounts are owned by the marriage regardless of how they're titled. I would imagine legal debts are similar. There's some exceptions and I suppose gambling debt could be one, but I would expect the default to be that the debt holder could collect from assets held by either spouse.
This will vary greatly from one jurisdiction to another. It can also depend on the specific kind of marriage.
Yes, some marriages are "community of property", some are not. Even in community of property though some debts may be on the individual not the couple.
So one cannot really talk in generalities regarding this.